# Jacobsthal numbers

Jacobsthal numbers
You are encouraged to solve this task according to the task description, using any language you may know.

Jacobsthal numbers are an integer sequence related to Fibonacci numbers. Similar to Fibonacci, where each term is the sum of the previous two terms, each term is the sum of the previous, plus twice the one before that. Traditionally the sequence starts with the given terms 0, 1.

```
J0 = 0
J1 = 1
Jn = Jn-1 + 2 × Jn-2

```

Terms may be calculated directly using one of several possible formulas:

```
Jn = ( 2n - (-1)n ) / 3

```

Jacobsthal-Lucas numbers are very similar. They have the same recurrence relationship, the only difference is an initial starting value J0 = 2 rather than J0 = 0.

Terms may be calculated directly using one of several possible formulas:

```
JLn = 2n + (-1)n

```

Jacobsthal oblong numbers is the sequence obtained from multiplying each Jacobsthal number Jn by its direct successor Jn+1.

Jacobsthal primes are Jacobsthal numbers that are prime.

• Find and display the first 30 Jacobsthal numbers
• Find and display the first 30 Jacobsthal-Lucas numbers
• Find and display the first 20 Jacobsthal oblong numbers
• Find and display at least the first 10 Jacobsthal primes

## 11l

Translation of: Python
```F isPrime(n)
L(i) 2 .. Int(n ^ 0.5)
I n % i == 0
R 0B
R 1B

F odd(n)
R n [&] 1 != 0

F jacobsthal(n)
R floori((pow(2.0, n) + odd(n)) / 3)

F jacobsthal_lucas(n)
R Int(pow(2, n) + pow(-1, n))

F jacobsthal_oblong(n)
R Int64(jacobsthal(n)) * jacobsthal(n + 1)

print(‘First 30 Jacobsthal numbers:’)
L(j) 0..29
print(jacobsthal(j), end' ‘  ’)

print("\n\nFirst 30 Jacobsthal-Lucas numbers: ")
L(j) 0..29
print(jacobsthal_lucas(j), end' "\t")

print("\n\nFirst 20 Jacobsthal oblong numbers: ")
L(j) 0..19
print(jacobsthal_oblong(j), end' ‘  ’)

print("\n\nFirst 10 Jacobsthal primes: ")
L(j) 3..32
I isPrime(jacobsthal(j))
print(jacobsthal(j))```
Output:
```First 30 Jacobsthal numbers:
0  1  1  3  5  11  21  43  85  171  341  683  1365  2731  5461  10923  21845  43691  87381  174763  349525  699051  1398101  2796203  5592405  11184811  22369621  44739243  89478485  178956971

First 30 Jacobsthal-Lucas numbers:
2	1	5	7	17	31	65	127	257	511	1025	2047	4097	8191	16385	32767	65537	131071	262145	524287	1048577	2097151	4194305	8388607	16777217	33554431	67108865	134217727	268435457	536870911

First 20 Jacobsthal oblong numbers:
0  1  3  15  55  231  903  3655  14535  58311  232903  932295  3727815  14913991  59650503  238612935  954429895  3817763271  15270965703  61084037575

First 10 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
```

## ALGOL 68

Works with: ALGOL 68G version Any - tested with release 2.8.3.win32
```BEGIN # find some Jacobsthal and related Numbers                             #
INT max jacobsthal = 29;        # highest Jacobsthal number we will find #
INT max oblong     = 20; # highest Jacobsthal oblong number we will find #
INT max j prime    = 20;     # number of Jacobsthal prinmes we will find #
PR precision 200 PR                 # set the precision of LONG LONG INT #
PR read "primes.incl.a68" PR                   # include prime utilities #
[ 0 : max jacobsthal ]LONG INT j;         # will hold Jacobsthal numbers #
[ 0 : max jacobsthal ]LONG INT jl;  # will hold Jacobsthal-Lucas numbers #
[ 1 : max oblong     ]LONG INT jo; # will hold Jacobsthal oblong numbers #
# calculate the Jacobsthal Numbers and related numbers                   #
# Jacobsthal      : J0  = 0, J1  = 1, Jn  = Jn-1  + 2 × Jn-2             #
# Jacobsthal-Lucas: JL0 = 2, JL1 = 1, JLn = JLn-1 + 2 × JLn-2            #
# Jacobsthal oblong: JOn = Jn x Jn-1                                     #
j[ 0 ] := 0; j[ 1 ] := 1; jl[ 0 ] := 2; jl[ 1 ] := 1; jo[ 1 ] := 0;
FOR n FROM 2 TO UPB j DO
j[  n ] := j[  n - 1 ] + ( 2 * j[  n - 2 ] );
jl[ n ] := jl[ n - 1 ] + ( 2 * jl[ n - 2 ] )
OD;
FOR n TO UPB jo DO
jo[ n ] := j[ n ] * j[ n - 1 ]
OD;
# prints an array of numbers with the specified legend                   #
PROC show numbers = ( STRING legend, []LONG INT numbers )VOID:
BEGIN
INT n count := 0;
print( ( "First ", whole( ( UPB numbers - LWB numbers ) + 1, 0 ), " ", legend, newline ) );
FOR n FROM LWB numbers TO UPB numbers DO
print( ( " ", whole( numbers[ n ], -11 ) ) );
IF ( n count +:= 1 ) MOD 5 = 0 THEN print( ( newline ) ) FI
OD
END # show numbers # ;
# show the various numbers numbers                                       #
show numbers( "Jacobsthal Numbers:",        j  );
show numbers( "Jacobsthal-Lucas Numbers:",  jl );
show numbers( "Jacobsthal oblong Numbers:", jo );
# find some prime Jacobsthal numbers                                     #
LONG LONG INT  jn1 := j[ 1 ], jn2 := j[ 0 ];
INT  p count := 0;
print( ( "First ", whole( max j prime, 0 ), " Jacobstal primes:", newline ) );
print( ( "   n  Jn", newline ) );
FOR n FROM 2 WHILE p count < max j prime DO
LONG LONG INT jn = jn1 + ( 2 * jn2 );
jn2        := jn1;
jn1        := jn;
IF is probably prime( jn ) THEN
# have a probably prime Jacobsthal number                        #
p count +:= 1;
print( ( whole( n, -4 ), ": ", whole( jn, 0 ), newline ) )
FI
OD
END```
Output:
```First 30 Jacobsthal Numbers:
0           1           1           3           5
11          21          43          85         171
341         683        1365        2731        5461
10923       21845       43691       87381      174763
349525      699051     1398101     2796203     5592405
11184811    22369621    44739243    89478485   178956971
First 30 Jacobsthal-Lucas Numbers:
2           1           5           7          17
31          65         127         257         511
1025        2047        4097        8191       16385
32767       65537      131071      262145      524287
1048577     2097151     4194305     8388607    16777217
33554431    67108865   134217727   268435457   536870911
First 20 Jacobsthal oblong Numbers:
0           1           3          15          55
231         903        3655       14535       58311
232903      932295     3727815    14913991    59650503
238612935   954429895  3817763271 15270965703 61084037575
First 20 Jacobstal primes:
n  Jn
3: 3
4: 5
5: 11
7: 43
11: 683
13: 2731
17: 43691
19: 174763
23: 2796203
31: 715827883
43: 2932031007403
61: 768614336404564651
79: 201487636602438195784363
101: 845100400152152934331135470251
127: 56713727820156410577229101238628035243
167: 62357403192785191176690552862561408838653121833643
191: 1046183622564446793972631570534611069350392574077339085483
199: 267823007376498379256993682056860433753700498963798805883563
313: 5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
347: 95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443
```

## AppleScript

### Procedural

```on jacobsthalNumbers(variant, n)
-- variant: text containing "Lucas", "oblong", or "prime" — or none of these.
-- n: length of output sequence required.

-- The two Jacobsthal numbers preceding the current 'j'. Initially the first two in the sequence.
set {anteprev, prev} to {0, 1}
-- Default plug-in script. Its handler simply appends the current 'j' to the output.
script o
property output : {anteprev, prev}
on append(dummy, j)
set end of output to j
end append
end script

-- If a variant sequence is specified, change the first value or substitute
-- a script whose handler decides the values to append to the output.
ignoring case
if (variant contains "Lucas") then
set anteprev to 2
set o's output's first item to anteprev
else if (variant contains "oblong") then
script
property output : {0}
on append(prev, j)
set end of output to prev * j
end append
end script
set o to result
else if (variant contains "prime") then
script
property output : {}
on append(dummy, j)
if (isPrime(j)) then set end of output to j
end append
end script
set o to result
end if
end ignoring

-- Work through the Jacobsthal process until the required output length is obtained.
repeat until ((count o's output) = n)
set j to anteprev + anteprev + prev
tell o to append(prev, j)
set anteprev to prev
set prev to j
end repeat

return o's output
end jacobsthalNumbers

on isPrime(n)
if (n < 3) then return (n is 2)
if (n mod 2 is 0) then return false
repeat with i from 3 to (n ^ 0.5) div 1 by 2
if (n mod i is 0) then return false
end repeat
return true
end isPrime

-- Task and presentation of results!:
on intToText(n)
set txt to ""
repeat until (n < 100000000)
set txt to text 2 thru 9 of (100000000 + (n mod 100000000) div 1 as text) & txt
set n to n div 100000000
end repeat
return (n as integer as text) & txt
end intToText

on chopList(theList, sublistLen)
script o
property lst : theList
property output : {}
end script

set listLen to (count o's lst)
repeat with i from 1 to listLen by sublistLen
set j to i + sublistLen - 1
if (j > listLen) then set j to listLen
set end of o's output to items i thru j of o's lst
end repeat
return o's output
end chopList

on matrixToText(matrix, w)
script o
property matrix : missing value
property row : missing value
end script

set o's matrix to matrix
repeat with r from 1 to (count o's matrix)
set o's row to o's matrix's item r
repeat with i from 1 to (count o's row)
set o's row's item i to text -w thru end of (padding & o's row's item i)
end repeat
set o's matrix's item r to join(o's row, "")
end repeat

return join(o's matrix, linefeed)
end matrixToText

on join(lst, delim)
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to delim
set txt to lst as text
set AppleScript's text item delimiters to astid
return txt
end join

set output to {"First 30 Jacobsthal Numbers:", "First 30 Jacobsthal-Lucas Numbers:", ¬
"First 20 Jacobsthal oblong Numbers:", "First 11 Jacobsthal Primes:"}
set results to {jacobsthalNumbers("", 30), jacobsthalNumbers("Lucas", 30), ¬
jacobsthalNumbers("oblong", 20), jacobsthalNumbers("prime", 11)}
repeat with i from 1 to 4
set thisSequence to item i of results
repeat with j in thisSequence
set j's contents to intToText(j)
end repeat
if (i < 4) then
set theLines to chopList(thisSequence, 10)
else
set theLines to chopList(thisSequence, 6)
end if
set item i of output to item i of output & linefeed & matrixToText(theLines, (count end of thisSequence) + 1)
end repeat

return join(output, linefeed & linefeed)

```
Output:
```"First 30 Jacobsthal Numbers:
0         1         1         3         5        11        21        43        85       171
341       683      1365      2731      5461     10923     21845     43691     87381    174763
349525    699051   1398101   2796203   5592405  11184811  22369621  44739243  89478485 178956971

First 30 Jacobsthal-Lucas Numbers:
2         1         5         7        17        31        65       127       257       511
1025      2047      4097      8191     16385     32767     65537    131071    262145    524287
1048577   2097151   4194305   8388607  16777217  33554431  67108865 134217727 268435457 536870911

First 20 Jacobsthal oblong Numbers:
0           1           3          15          55         231         903        3655       14535       58311
232903      932295     3727815    14913991    59650503   238612935   954429895  3817763271 15270965703 61084037575

First 11 Jacobsthal Primes:
3             5            11            43           683          2731
43691        174763       2796203     715827883 2932031007403"
```

### Functional

```-------------------- JACOBSTHAL NUMBERS ------------------

-- e.g. take(10, jacobsthal())

-- jacobsthal :: [Int]
on jacobsthal()
-- The terms of OEIS:A001045 as a non-finite sequence.
jacobsthalish(0, 1)
end jacobsthal

-- jacobsthal :: (Int, Int) -> [Int]
on jacobsthalish(x, y)
-- An infinite sequence of the terms of the
-- Jacobsthal-type series which begins with x and y.
script go
on |λ|(ab)
set {a, b} to ab

{a, {b, (2 * a) + b}}
end |λ|
end script

unfoldr(go, {x, y})
end jacobsthalish

-------------------------- TESTS -------------------------
on run
unlines(map(fShow, {¬
{"terms of the Jacobsthal sequence", ¬
30, jacobsthal()}, ¬
{"Jacobsthal-Lucas numbers", ¬
30, jacobsthalish(2, 1)}, ¬
{"Jacobsthal oblong numbers", ¬
20, zipWith(my mul, jacobsthal(), drop(1, jacobsthal()))}, ¬
{"primes in the Jacobsthal sequence", ¬
10, filter(isPrime, jacobsthal())}}))
end run

------------------------ FORMATTING ----------------------
on fShow(test)
set {k, n, xs} to test

str(n) & " first " & k & ":" & linefeed & ¬
table(5, map(my str, take(n, xs))) & linefeed
end fShow

-- justifyRight :: Int -> Char -> String -> String
on justifyRight(n, cFiller)
script go
on |λ|(s)
if n > length of s then
text -n thru -1 of ((replicate(n, cFiller) as text) & s)
else
s
end if
end |λ|
end script
end justifyRight

-- Egyptian multiplication - progressively doubling a list, appending
-- stages of doubling to an accumulator where needed for binary
-- assembly of a target length
-- replicate :: Int -> String -> String
on replicate(n, s)
-- Egyptian multiplication - progressively doubling a list,
-- appending stages of doubling to an accumulator where needed
-- for binary assembly of a target length
script p
on |λ|({n})
n ≤ 1
end |λ|
end script

script f
on |λ|({n, dbl, out})
if (n mod 2) > 0 then
set d to out & dbl
else
set d to out
end if
{n div 2, dbl & dbl, d}
end |λ|
end script

set xs to |until|(p, f, {n, s, ""})
item 2 of xs & item 3 of xs
end replicate

-- table :: Int -> [String] -> String
on table(n, xs)
-- A list of strings formatted as
-- right-justified rows of n columns.
set w to length of last item of xs
unlines(map(my unwords, ¬
chunksOf(n, map(justifyRight(w, space), xs))))
end table

-- unlines :: [String] -> String
on unlines(xs)
-- A single string formed by the intercalation
-- of a list of strings with the newline character.
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set s to xs as text
set my text item delimiters to dlm
s
end unlines

-- until :: (a -> Bool) -> (a -> a) -> a -> a
on |until|(p, f, x)
set v to x
set mp to mReturn(p)
set mf to mReturn(f)
repeat until mp's |λ|(v)
set v to mf's |λ|(v)
end repeat
v
end |until|

-- unwords :: [String] -> String
on unwords(xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, space}
set s to xs as text
set my text item delimiters to dlm
return s
end unwords

------------------------- GENERIC ------------------------

-- Just :: a -> Maybe a
on Just(x)
-- Constructor for an inhabited Maybe (option type) value.
-- Wrapper containing the result of a computation.
{type:"Maybe", Nothing:false, Just:x}
end Just

-- Nothing :: Maybe a
on Nothing()
-- Constructor for an empty Maybe (option type) value.
-- Empty wrapper returned where a computation is not possible.
{type:"Maybe", Nothing:true}
end Nothing

-- abs :: Num -> Num
on abs(x)
-- Absolute value.
if 0 > x then
-x
else
x
end if
end abs

-- any :: (a -> Bool) -> [a] -> Bool
on any(p, xs)
-- Applied to a predicate and a list,
-- |any| returns true if at least one element of the
-- list satisfies the predicate.
tell mReturn(p)
set lng to length of xs
repeat with i from 1 to lng
if |λ|(item i of xs) then return true
end repeat
false
end tell
end any

-- chunksOf :: Int -> [a] -> [[a]]
on chunksOf(k, xs)
script
on go(ys)
set ab to splitAt(k, ys)
set a to item 1 of ab
if {} ≠ a then
{a} & go(item 2 of ab)
else
a
end if
end go
end script
result's go(xs)
end chunksOf

-- drop :: Int -> [a] -> [a]
-- drop :: Int -> String -> String
on drop(n, xs)
take(n, xs) -- consumed
xs
end drop

-- enumFromThenTo :: Int -> Int -> Int -> [Int]
on enumFromThenTo(x1, x2, y)
set xs to {}
set gap to x2 - x1
set d to max(1, abs(gap)) * (signum(gap))
repeat with i from x1 to y by d
set end of xs to i
end repeat
return xs
end enumFromThenTo

-- filter :: (a -> Bool) -> Gen [a] -> Gen [a]
on filter(p, gen)
-- Non-finite stream of values which are
-- drawn from gen, and satisfy p
script
property mp : mReturn(p)'s |λ|
on |λ|()
set v to gen's |λ|()
repeat until mp(v)
set v to gen's |λ|()
end repeat
return v
end |λ|
end script
end filter

-- isPrime :: Int -> Bool
on isPrime(n)
-- True if n is prime

if {2, 3} contains n then return true

if 2 > n or 0 = (n mod 2) then return false

if 9 > n then return true

if 0 = (n mod 3) then return false

script p
on |λ|(x)
0 = n mod x or 0 = n mod (2 + x)
end |λ|
end script

not any(p, enumFromThenTo(5, 11, 1 + (n ^ 0.5)))
end isPrime

-- length :: [a] -> Int
on |length|(xs)
set c to class of xs
if list is c or string is c then
length of xs
else
(2 ^ 29 - 1) -- (maxInt - simple proxy for non-finite)
end if
end |length|

-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
-- The list obtained by applying f
-- to each element of xs.
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map

-- max :: Ord a => a -> a -> a
on max(x, y)
if x > y then
x
else
y
end if
end max

-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
-- 2nd class handler function lifted into 1st class script wrapper.
if script is class of f then
f
else
script
property |λ| : f
end script
end if
end mReturn

-- mul (*) :: Num a => a -> a -> a
on mul(a, b)
a * b
end mul

-- signum :: Num -> Num
on signum(x)
if x < 0 then
-1
else if x = 0 then
0
else
1
end if
end signum

-- splitAt :: Int -> [a] -> ([a], [a])
on splitAt(n, xs)
if n > 0 and n < length of xs then
if class of xs is text then
{items 1 thru n of xs as text, ¬
items (n + 1) thru -1 of xs as text}
else
{items 1 thru n of xs, items (n + 1) thru -1 of xs}
end if
else
if n < 1 then
{{}, xs}
else
{xs, {}}
end if
end if
end splitAt

-- str :: a -> String
on str(x)
x as string
end str

-- take :: Int -> [a] -> [a]
-- take :: Int -> String -> String
on take(n, xs)
set ys to {}
repeat with i from 1 to n
set v to |λ|() of xs
if missing value is v then
return ys
else
set end of ys to v
end if
end repeat
return ys
end take

-- uncons :: [a] -> Maybe (a, [a])
on uncons(xs)
set lng to |length|(xs)
if 0 = lng then
Nothing()
else
if (2 ^ 29 - 1) as integer > lng then
if class of xs is string then
set cs to text items of xs
Just({item 1 of cs, rest of cs})
else
Just({item 1 of xs, rest of xs})
end if
else
set nxt to take(1, xs)
if {} is nxt then
Nothing()
else
Just({item 1 of nxt, xs})
end if
end if
end if
end uncons

-- unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
on unfoldr(f, v)
-- A lazy (generator) list unfolded from a seed value
-- by repeated application of f to a value until no
-- residue remains. Dual to fold/reduce.
-- f returns either nothing (missing value)
-- or just (value, residue).
script
property valueResidue : {v, v}
property g : mReturn(f)
on |λ|()
set valueResidue to g's |λ|(item 2 of (valueResidue))
if missing value ≠ valueResidue then
item 1 of (valueResidue)
else
missing value
end if
end |λ|
end script
end unfoldr

-- zipWith :: (a -> b -> c) -> Gen [a] -> Gen [b] -> Gen [c]
on zipWith(f, ga, gb)
script
property ma : missing value
property mb : missing value
property mf : mReturn(f)
on |λ|()
if missing value is ma then
set ma to uncons(ga)
set mb to uncons(gb)
end if
if Nothing of ma or Nothing of mb then
missing value
else
set ta to Just of ma
set tb to Just of mb
set ma to uncons(item 2 of ta)
set mb to uncons(item 2 of tb)
|λ|(item 1 of ta, item 1 of tb) of mf
end if
end |λ|
end script
end zipWith
```
Output:
```30 first terms of the Jacobsthal sequence:
0         1         1         3         5
11        21        43        85       171
341       683      1365      2731      5461
10923     21845     43691     87381    174763
349525    699051   1398101   2796203   5592405
11184811  22369621  44739243  89478485 178956971

30 first Jacobsthal-Lucas numbers:
2         1         5         7        17
31        65       127       257       511
1025      2047      4097      8191     16385
32767     65537    131071    262145    524287
1048577   2097151   4194305   8388607  16777217
33554431  67108865 134217727 268435457 536870911

20 first Jacobsthal oblong numbers:
0                1                3               15               55
231              903             3655            14535            58311
232903           932295          3727815         14913991         59650503
238612935    9.54429895E+8   3.817763271E+9 1.5270965703E+10 6.1084037575E+10

10 first primes in the Jacobsthal sequence:
3             5            11            43           683
2731         43691        174763       2796203 7.15827883E+8```

## Arturo

```J:  function [n]-> ((2^n) - (neg 1)^n)/3
JL: function [n]-> (2^n) + (neg 1)^n
JO: function [n]-> (J n) * (J n+1)

printFirst: function [label, what, predicate, count][
print ["First" count label++":"]
result: new []
i: 0
while [count > size result][
num: do ~"|what| i"
if do predicate -> 'result ++ num
i: i + 1
]

(predicate=[true])? [
loop split.every: 5 result 'row [
print map to [:string] row 'item -> pad item 12
]
][
loop result 'row -> print row
]
print ""
]

printFirst "Jacobsthal numbers" 'J [true] 30
printFirst "Jacobsthal-Lucas numbers" 'JL [true] 30
printFirst "Jacobsthal oblong numbers" 'JO [true] 20
printFirst "Jacobsthal primes" 'J [prime? num] 20
```
Output:
```First 30 Jacobsthal numbers:
0            1            1            3            5
11           21           43           85          171
341          683         1365         2731         5461
10923        21845        43691        87381       174763
349525       699051      1398101      2796203      5592405
11184811     22369621     44739243     89478485    178956971

First 30 Jacobsthal-Lucas numbers:
2            1            5            7           17
31           65          127          257          511
1025         2047         4097         8191        16385
32767        65537       131071       262145       524287
1048577      2097151      4194305      8388607     16777217
33554431     67108865    134217727    268435457    536870911

First 20 Jacobsthal oblong numbers:
0            1            3           15           55
231          903         3655        14535        58311
232903       932295      3727815     14913991     59650503
238612935    954429895   3817763271  15270965703  61084037575

First 20 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
2932031007403
768614336404564651
201487636602438195784363
845100400152152934331135470251
56713727820156410577229101238628035243
62357403192785191176690552862561408838653121833643
1046183622564446793972631570534611069350392574077339085483
267823007376498379256993682056860433753700498963798805883563
5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443```

## AutoHotkey

```Jacobsthal(n){
return SubStr("        " Format("{:.0f}", (2**n - (-1)**n ) / 3), -8)
}

Jacobsthal_Lucas(n){
return SubStr("        " Format("{:.0f}", 2**n + (-1)**n), -8)
}

prime_numbers(n) {
if (n <= 3)
return [n]
ans := [], done := false
while !done {
if !Mod(n,2)
ans.push(2), n /= 2
else if !Mod(n,3)
ans.push(3), n /= 3
else if (n = 1)
return ans
else {
sr := sqrt(n), done := true, i := 6
while (i <= sr+6) {
if !Mod(n, i-1) { ; is n divisible by i-1?
ans.push(i-1), n /= i-1, done := false
break
}
if !Mod(n, i+1) { ; is n divisible by i+1?
ans.push(i+1), n /= i+1, done := false
break
}
i += 6
}}}
ans.push(n)
return ans
}
```

Examples:

```result := "First 30 Jacobsthal numbers:`n"
loop 30
result .= Jacobsthal(A_Index-1) (mod(A_Index, 5) ? " ":"`n")

result .= "`nFirst 30 Jacobsthal-Lucas numbers:`n"
loop 30
result .= Jacobsthal_Lucas(A_Index-1) (mod(A_Index, 5) ? " ":"`n")

result .= "`nFirst 20 Jacobsthal oblong numbers:`n"
loop 20
result .= SubStr("        " Jacobsthal(A_Index-1) * Jacobsthal(A_Index), -8) (mod(A_Index, 5) ? " ":"`n")

result .= "`nFirst 10 Jacobsthal primes:`n"
c:=0
while c < 10
if (prime_numbers(x:=Jacobsthal(A_Index)).Count() = 1 && x > 1)
result .= x (mod(++c, 5) ? " ":"`n")

MsgBox, 262144, , % result
return
```
Output:
```First 30 Jacobsthal numbers:
0         1         1         3         5
11        21        43        85       171
341       683      1365      2731      5461
10923     21845     43691     87381    174763
349525    699051   1398101   2796203   5592405
11184811  22369621  44739243  89478485 178956971

First 30 Jacobsthal-Lucas numbers:
2         1         5         7        17
31        65       127       257       511
1025      2047      4097      8191     16385
32767     65537    131071    262145    524287
1048577   2097151   4194305   8388607  16777217
33554431  67108865 134217727 268435457 536870911

First 20 Jacobsthal oblong numbers:
0         1         3        15        55
231       903      3655     14535     58311
232903    932295   3727815  14913991  59650503
238612935 954429895 817763271 270965703 084037575

First 10 Jacobsthal primes:
3         5        11        43       683
2731     43691    174763   2796203 715827883```

## C

Library: GMP
```#include <stdio.h>
#include <gmp.h>

void jacobsthal(mpz_t r, unsigned long n) {
mpz_t s;
mpz_init(s);
mpz_set_ui(r, 1);
mpz_mul_2exp(r, r, n);
mpz_set_ui(s, 1);
if (n % 2) mpz_neg(s, s);
mpz_sub(r, r, s);
mpz_div_ui(r, r, 3);
}

void jacobsthal_lucas(mpz_t r, unsigned long n) {
mpz_t a;
mpz_init(a);
mpz_set_ui(r, 1);
mpz_mul_2exp(r, r, n);
mpz_set_ui(a, 1);
if (n % 2) mpz_neg(a, a);
}

int main() {
int i, count;
mpz_t jac[30], j;
printf("First 30 Jacobsthal numbers:\n");
for (i = 0; i < 30; ++i) {
mpz_init(jac[i]);
jacobsthal(jac[i], i);
gmp_printf("%9Zd ", jac[i]);
if (!((i+1)%5)) printf("\n");
}

printf("\nFirst 30 Jacobsthal-Lucas numbers:\n");
mpz_init(j);
for (i = 0; i < 30; ++i) {
jacobsthal_lucas(j, i);
gmp_printf("%9Zd ", j);
if (!((i+1)%5)) printf("\n");
}

printf("\nFirst 20 Jacobsthal oblong numbers:\n");
for (i = 0; i < 20; ++i) {
mpz_mul(j, jac[i], jac[i+1]);
gmp_printf("%11Zd ", j);
if (!((i+1)%5)) printf("\n");
}

printf("\nFirst 20 Jacobsthal primes:\n");
for (i = 0, count = 0; count < 20; ++i) {
jacobsthal(j, i);
if (mpz_probab_prime_p(j, 15) > 0) {
gmp_printf("%Zd\n", j);
++count;
}
}

return 0;
}
```
Output:
```First 30 Jacobsthal numbers:
0         1         1         3         5
11        21        43        85       171
341       683      1365      2731      5461
10923     21845     43691     87381    174763
349525    699051   1398101   2796203   5592405
11184811  22369621  44739243  89478485 178956971

First 30 Jacobsthal-Lucas numbers:
2         1         5         7        17
31        65       127       257       511
1025      2047      4097      8191     16385
32767     65537    131071    262145    524287
1048577   2097151   4194305   8388607  16777217
33554431  67108865 134217727 268435457 536870911

First 20 Jacobsthal oblong numbers:
0           1           3          15          55
231         903        3655       14535       58311
232903      932295     3727815    14913991    59650503
238612935   954429895  3817763271 15270965703 61084037575

First 20 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
2932031007403
768614336404564651
201487636602438195784363
845100400152152934331135470251
56713727820156410577229101238628035243
62357403192785191176690552862561408838653121833643
1046183622564446793972631570534611069350392574077339085483
267823007376498379256993682056860433753700498963798805883563
5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443
```

## C#

Translation of: Java
```using System;
using System.Numerics;

public class JacobsthalNumbers
{
private static BigInteger currentJacobsthal = 0;
private static int latestIndex = 0;
private static readonly BigInteger Three = new BigInteger(3);
private const int Certainty = 20;
public static void Main(string[] args)
{
Console.WriteLine("The first 30 Jacobsthal Numbers:");
for (int i = 0; i < 6; i++)
{
for (int k = 0; k < 5; k++)
{
Console.Write(\$"{JacobsthalNumber(i * 5 + k), 15}");
}

Console.WriteLine();
}

Console.WriteLine();
Console.WriteLine("The first 30 Jacobsthal-Lucas Numbers:");
for (int i = 0; i < 6; i++)
{
for (int k = 0; k < 5; k++)
{
Console.Write(\$"{JacobsthalLucasNumber(i * 5 + k), 15}");
}

Console.WriteLine();
}

Console.WriteLine();
Console.WriteLine("The first 20 Jacobsthal oblong Numbers:");
for (int i = 0; i < 4; i++)
{
for (int k = 0; k < 5; k++)
{
Console.Write(\$"{JacobsthalOblongNumber(i * 5 + k), 15}");
}

Console.WriteLine();
}

Console.WriteLine();
Console.WriteLine("The first 10 Jacobsthal Primes:");
for (int i = 0; i < 10; i++)
{
}
}

private static BigInteger JacobsthalNumber(int index)
{
BigInteger value = new BigInteger(ParityValue(index));
return ((BigInteger.Parse("1") << index) - value) / Three;
}

private static long JacobsthalLucasNumber(int index)
{
return (1L << index) + ParityValue(index);
}

private static long JacobsthalOblongNumber(int index)
{
BigInteger nextJacobsthal = JacobsthalNumber(index + 1);
long result = (long)(currentJacobsthal * nextJacobsthal);
currentJacobsthal = nextJacobsthal;
return result;
}

{
BigInteger candidate = JacobsthalNumber(latestIndex++);
while (!candidate.IsProbablyPrime(Certainty))
{
candidate = JacobsthalNumber(latestIndex++);
}

return (long)candidate;
}

private static int ParityValue(int index)
{
return (index & 1) == 0 ? +1 : -1;
}
}

public static class BigIntegerExtensions
{
private static Random random = new Random();

public static bool IsProbablyPrime(this BigInteger source, int certainty)
{
if (source == 2 || source == 3)
return true;
if (source < 2 || source % 2 == 0)
return false;

BigInteger d = source - 1;
int s = 0;

while (d % 2 == 0)
{
d /= 2;
s += 1;
}

for (int i = 0; i < certainty; i++)
{
BigInteger a = RandomBigInteger(2, source - 2);
BigInteger x = BigInteger.ModPow(a, d, source);
if (x == 1 || x == source - 1)
continue;

for (int r = 1; r < s; r++)
{
x = BigInteger.ModPow(x, 2, source);
if (x == 1)
return false;
if (x == source - 1)
break;
}

if (x != source - 1)
return false;
}

return true;
}

private static BigInteger RandomBigInteger(BigInteger minValue, BigInteger maxValue)
{
if (minValue > maxValue)
throw new ArgumentException("minValue must be less than or equal to maxValue");

BigInteger range = maxValue - minValue + 1;
int length = range.ToByteArray().Length;
byte[] buffer = new byte[length];

BigInteger result;
do
{
random.NextBytes(buffer);
buffer[buffer.Length - 1] &= 0x7F; // Ensure non-negative
result = new BigInteger(buffer);
} while (result < minValue || result >= maxValue);

return result;
}
}
```
Output:
```The first 30 Jacobsthal Numbers:
0              1              1              3              5
11             21             43             85            171
341            683           1365           2731           5461
10923          21845          43691          87381         174763
349525         699051        1398101        2796203        5592405
11184811       22369621       44739243       89478485      178956971

The first 30 Jacobsthal-Lucas Numbers:
2              1              5              7             17
31             65            127            257            511
1025           2047           4097           8191          16385
32767          65537         131071         262145         524287
1048577        2097151        4194305        8388607       16777217
33554431       67108865      134217727      268435457      536870911

The first 20 Jacobsthal oblong Numbers:
0              1              3             15             55
231            903           3655          14535          58311
232903         932295        3727815       14913991       59650503
238612935      954429895     3817763271    15270965703    61084037575

The first 10 Jacobsthal Primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883

```

## C++

Library: GMP
```#include <gmpxx.h>

#include <iomanip>
#include <iostream>

using big_int = mpz_class;

bool is_probably_prime(const big_int& n) {
return mpz_probab_prime_p(n.get_mpz_t(), 30) != 0;
}

big_int jacobsthal_number(unsigned int n) {
return ((big_int(1) << n) - (n % 2 == 0 ? 1 : -1)) / 3;
}

big_int jacobsthal_lucas_number(unsigned int n) {
return (big_int(1) << n) + (n % 2 == 0 ? 1 : -1);
}

big_int jacobsthal_oblong_number(unsigned int n) {
return jacobsthal_number(n) * jacobsthal_number(n + 1);
}

int main() {
std::cout << "First 30 Jacobsthal Numbers:\n";
for (unsigned int n = 0; n < 30; ++n) {
std::cout << std::setw(9) << jacobsthal_number(n)
<< ((n + 1) % 5 == 0 ? '\n' : ' ');
}
std::cout << "\nFirst 30 Jacobsthal-Lucas Numbers:\n";
for (unsigned int n = 0; n < 30; ++n) {
std::cout << std::setw(9) << jacobsthal_lucas_number(n)
<< ((n + 1) % 5 == 0 ? '\n' : ' ');
}
std::cout << "\nFirst 20 Jacobsthal oblong Numbers:\n";
for (unsigned int n = 0; n < 20; ++n) {
std::cout << std::setw(11) << jacobsthal_oblong_number(n)
<< ((n + 1) % 5 == 0 ? '\n' : ' ');
}
std::cout << "\nFirst 20 Jacobsthal primes:\n";
for (unsigned int n = 0, count = 0; count < 20; ++n) {
auto jn = jacobsthal_number(n);
if (is_probably_prime(jn)) {
++count;
std::cout << jn << '\n';
}
}
}
```
Output:
```First 30 Jacobsthal Numbers:
0         1         1         3         5
11        21        43        85       171
341       683      1365      2731      5461
10923     21845     43691     87381    174763
349525    699051   1398101   2796203   5592405
11184811  22369621  44739243  89478485 178956971

First 30 Jacobsthal-Lucas Numbers:
2         1         5         7        17
31        65       127       257       511
1025      2047      4097      8191     16385
32767     65537    131071    262145    524287
1048577   2097151   4194305   8388607  16777217
33554431  67108865 134217727 268435457 536870911

First 20 Jacobsthal oblong Numbers:
0           1           3          15          55
231         903        3655       14535       58311
232903      932295     3727815    14913991    59650503
238612935   954429895  3817763271 15270965703 61084037575

First 20 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
2932031007403
768614336404564651
201487636602438195784363
845100400152152934331135470251
56713727820156410577229101238628035243
62357403192785191176690552862561408838653121833643
1046183622564446793972631570534611069350392574077339085483
267823007376498379256993682056860433753700498963798805883563
5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443
```

## Delphi

Works with: Delphi version 6.0

```procedure GetJacobsthalNum(Lucas: boolean; Max: integer; var IA: TInt64DynArray);
{Get Jacobsthal number sequence. If Lucas is true do Lucal variation}
var I: integer;
begin
SetLength(IA,Max);
{Lucas starts sequence with 2 instead of 0}
if Lucas then IA[0]:=2 else IA[0]:=0;
IA[1]:=1;
{Calculate Nn = Nn-1 + 2 Nn-2}
for I:=2 to Max-1 do
IA[I]:=IA[I-1] + 2 * IA[I-2];
end;

procedure GetJacobsthalOblong(Max: integer; var IA: TInt64DynArray);
{Jacobsthal Oblong numbers is Nn = Jn x Jn=1 where J = Jacobsthal numbers}
var IA2: TInt64DynArray;
var I: integer;
begin
GetJacobsthalNum(False,Max+1,IA2);
SetLength(IA,Max);
for I:=0 to High(IA2)-1 do
begin
IA[I]:=IA2[I] * IA2[I+1];
end;
end;

procedure GetJacobsthalPrimes(Memo: TMemo);
var I: integer;
var Jacob,N1, N2: int64;

function GetNext: int64;
{Nn = Nn-1 + 2 x Nn-2}
begin
Result:=N1 + 2 * N2;
N2:=N1; N1:=Result;
end;

begin
N2:=0; N1:=1;
for I:=1 to 10 do
begin
repeat Jacob:=GetNext;
until IsPrime(Jacob);
end;
end;

procedure ShowJacobsthalNumbers(Memo: TMemo);
var I: integer;
var IA: TInt64DynArray;
var S: string;
begin
GetJacobsthalNum(False,30,IA);
S:='';
for I:=0 to High(IA) do
begin
S:=S+Format('%12.0n',[IA[I]+0.0]);
if (I mod 5)=4 then S:=S+CRLF;
end;

GetJacobsthalNum(True,30,IA);
S:='';
for I:=0 to High(IA) do
begin
S:=S+Format('%14.0n',[IA[I]+0.0]);
if (I mod 4)=3 then S:=S+CRLF;
end;

GetJacobsthalOblong(20,IA);
S:='';
for I:=0 to High(IA) do
begin
S:=S+Format('%18.0n',[IA[I]+0.0]);
if (I mod 3)=2 then S:=S+CRLF;
end;

GetJacobsthalPrimes(Memo);
end;
```
Output:
```First 30 Jacobsthal Numbers
0           1           1           3           5
11          21          43          85         171
341         683       1,365       2,731       5,461
10,923      21,845      43,691      87,381     174,763
349,525     699,051   1,398,101   2,796,203   5,592,405
11,184,811  22,369,621  44,739,243  89,478,485 178,956,971

First 30 Jacobsthal-Lucas Numbers
2             1             5             7
17            31            65           127
257           511         1,025         2,047
4,097         8,191        16,385        32,767
65,537       131,071       262,145       524,287
1,048,577     2,097,151     4,194,305     8,388,607
16,777,217    33,554,431    67,108,865   134,217,727
268,435,457   536,870,911

First 20 Jacobsthal-Oblong Numbers
0                 1                 3
15                55               231
903             3,655            14,535
58,311           232,903           932,295
3,727,815        14,913,991        59,650,503
238,612,935       954,429,895     3,817,763,271
15,270,965,703    61,084,037,575

1 - 3
2 - 5
3 - 11
4 - 43
5 - 683
6 - 2731
7 - 43691
8 - 174763
9 - 2796203
10 - 715827883

Elapsed Time: 49.627 ms.

```

## F#

```// Jacobsthal numbers: Nigel Galloway January 10th., 2023
let J,JL=let fN g ()=Seq.unfold(fun(n,g)->Some(n,(g,g+2UL*n)))(g,1UL) in (fN 0UL,fN 2UL)
printf "First 30 Jacobsthal are "; J()|>Seq.take 30|>Seq.iter(printf "%d "); printfn ""
printf "First 30 Jacobsthal-Lucas are "; JL()|>Seq.take 30|>Seq.iter(printf "%d "); printfn ""
printf "First 20 Jacobsthal Oblong are "; J()|>Seq.pairwise|>Seq.take 20|>Seq.iter(fun(n,g)->printf "%d " (n*g)); printfn ""
let fN g= Open.Numeric.Primes.MillerRabin.IsPrime &g
printf "First 10 Jacobsthal Primes are "; J()|>Seq.filter fN|>Seq.take 10|>Seq.iter(printf "%d "); printfn ""
```
Output:
```First 30 Jacobsthal are 0 1 1 3 5 11 21 43 85 171 341 683 1365 2731 5461 10923 21845 43691 87381 174763 349525 699051 1398101 2796203 5592405 11184811 22369621 44739243 89478485 178956971
First 30 Jacobsthal-Lucas are 2 1 5 7 17 31 65 127 257 511 1025 2047 4097 8191 16385 32767 65537 131071 262145 524287 1048577 2097151 4194305 8388607 16777217 33554431 67108865 134217727 268435457 536870911
First 20 Jacobsthal Oblong are 0 1 3 15 55 231 903 3655 14535 58311 232903 932295 3727815 14913991 59650503 238612935 954429895 3817763271 15270965703 61084037575
First 10 Jacobsthal Primes are 3 5 11 43 683 2731 43691 174763 2796203 715827883
```

## Factor

Works with: Factor version 0.99 2021-06-02
```USING: grouping io kernel lists lists.lazy math math.functions
math.primes prettyprint sequences ;

: 2^-1^ ( n -- 2^n -1^n ) dup 2^ -1 rot ^ ;
: jacobsthal ( m -- n ) 2^-1^ - 3 / ;
: jacobsthal-lucas ( m -- n ) 2^-1^ + ;
: as-list ( quot -- list ) 0 lfrom swap lmap-lazy ; inline
: jacobsthals ( -- list ) [ jacobsthal ] as-list ;
: lucas-jacobthals ( -- list ) [ jacobsthal-lucas ] as-list ;
: prime-jacobsthals ( -- list ) jacobsthals [ prime? ] lfilter ;
: show ( n list -- ) ltake list>array 5 group simple-table. nl ;

: oblong ( -- list )
jacobsthals dup cdr lzip [ product ] lmap-lazy ;

"First 30 Jacobsthal numbers:" print
30 jacobsthals show

"First 30 Jacobsthal-Lucas numbers:" print
30 lucas-jacobthals show

"First 20 Jacobsthal oblong numbers:" print
20 oblong show

"First 20 Jacobsthal primes:" print
20 prime-jacobsthals ltake [ . ] leach
```
Output:
```First 30 Jacobsthal numbers:
0        1        1        3        5
11       21       43       85       171
341      683      1365     2731     5461
10923    21845    43691    87381    174763
349525   699051   1398101  2796203  5592405
11184811 22369621 44739243 89478485 178956971

First 30 Jacobsthal-Lucas numbers:
2        1        5         7         17
31       65       127       257       511
1025     2047     4097      8191      16385
32767    65537    131071    262145    524287
1048577  2097151  4194305   8388607   16777217
33554431 67108865 134217727 268435457 536870911

First 20 Jacobsthal oblong numbers:
0         1         3          15          55
231       903       3655       14535       58311
232903    932295    3727815    14913991    59650503
238612935 954429895 3817763271 15270965703 61084037575

First 20 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
2932031007403
768614336404564651
201487636602438195784363
845100400152152934331135470251
56713727820156410577229101238628035243
62357403192785191176690552862561408838653121833643
1046183622564446793972631570534611069350392574077339085483
267823007376498379256993682056860433753700498963798805883563
5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443
```

## FreeBASIC

```Function isPrime(n As Ulongint) As Boolean
If n < 2 Then Return False
If n Mod 2 = 0 Then Return false
For i As Uinteger = 3 To Int(Sqr(n))+1 Step 2
If n Mod i = 0 Then Return false
Next i
Return true
End Function

Dim Shared As Uinteger n(1)
Dim Shared As Uinteger i0 = 0, i1 = 1
Dim Shared As Integer j, c, P = 1, Q = -2

Print "First 30 Jacobsthal numbers:"
c = 0 : n(i0) = 0: n(i1) = 1
For j = 0 To 29
c += 1
Print Using " #########"; n(i0);
Print Iif (c Mod 5, "", !"\n");
n(i0) = P * n(i1) - Q * n(i0)
Swap i0, i1
Next j

Print !"\n\nFirst 30 Jacobsthal-Lucas numbers: "
c = 0 : n(i0) = 2: n(i1) = 1
For j = 0 To 29
c += 1
Print Using " #########"; n(i0);
Print Iif (c Mod 5, "", !"\n");
n(i0) = P * n(i1) - Q * n(i0)
Swap i0, i1
Next j

Print !"\n\nFirst 20 Jacobsthal oblong numbers: "
c = 0 : n(i0) = 0: n(i1) = 1
For j = 0 To 19
c += 1
Print Using " ###########"; n(i0)*n(i1);
Print Iif (c Mod 5, "", !"\n");
n(i0) = P * n(i1) - Q * n(i0)
Swap i0, i1
Next j

Print !"\n\nFirst 10 Jacobsthal primes: "
c = 0 : n(i0) = 0: n(i1) = 1
Do
If isPrime(n(i0)) Then c += 1 : Print n(i0)
n(i0) = P * n(i1) - Q * n(i0)
Swap i0, i1
Loop Until c = 10
Sleep```
Output:
```First 30 Jacobsthal numbers:
0         1         1         3         5
11        21        43        85       171
341       683      1365      2731      5461
10923     21845     43691     87381    174763
349525    699051   1398101   2796203   5592405
11184811  22369621  44739243  89478485 178956971

First 30 Jacobsthal-Lucas numbers:
2         1         5         7        17
31        65       127       257       511
1025      2047      4097      8191     16385
32767     65537    131071    262145    524287
1048577   2097151   4194305   8388607  16777217
33554431  67108865 134217727 268435457 536870911

First 20 Jacobsthal oblong numbers:
0           1           3          15          55
231         903        3655       14535       58311
232903      932295     3727815    14913991    59650503
238612935   954429895  3817763271 15270965703 61084037575

First 10 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883```

## Gambas

```Public n As New Long[2]

Public Sub Main()

Dim i0 As Integer = 0, i1 As Integer = 1
Dim j As Integer, c As Integer, P As Integer = 1, Q As Integer = -2

Print "First 30 Jacobsthal numbers:"
c = 0
n[i0] = 0
n[i1] = 1
For j = 0 To 29
c += 1
Print Format\$(n[i0], " #########");
If (c Mod 5) Then
Print "";
Else
Print Chr(10);
End If
n[i0] = P * n[i1] - Q * n[i0]
Swap i0, i1
Next

Print "\n\nFirst 30 Jacobsthal-Lucas numbers: "
c = 0
n[i0] = 2
n[i1] = 1
For j = 0 To 29
c += 1
Print Format\$(n[i0], " #########");
If (c Mod 5) Then
Print "";
Else
Print Chr(10);
End If
n[i0] = P * n[i1] - Q * n[i0]
Swap i0, i1
Next

Print "\n\nFirst 20 Jacobsthal oblong numbers: "
c = 0
n[i0] = 0
n[i1] = 1
For j = 0 To 19
c += 1
Print Format\$(n[i0] * n[i1], " ###########");
If (c Mod 5) Then
Print "";
Else
Print Chr(10);
End If
n[i0] = P * n[i1] - Q * n[i0]
Swap i0, i1
Next

Print "\n\nFirst 10 Jacobsthal primes: "
c = 0
n[i0] = 0
n[i1] = 1
Do
If isPrime(n[i0]) Then
c += 1
Print n[i0]
End If
n[i0] = P * n[i1] - Q * n[i0]
Swap i0, i1
Loop Until c = 10

End

Public Sub isPrime(ValorEval As Long) As Boolean

If ValorEval < 2 Then Return False
If ValorEval Mod 2 = 0 Then Return ValorEval = 2
If ValorEval Mod 3 = 0 Then Return ValorEval = 3
Dim d As Long = 5
While d * d <= ValorEval
If ValorEval Mod d = 0 Then Return False Else d += 2
Wend
Return True

End Function
```
Output:
`Same as FreeBASIC entry.`

## Go

```package main

import (
"fmt"
"math/big"
)

func jacobsthal(n uint) *big.Int {
t := big.NewInt(1)
t.Lsh(t, n)
s := big.NewInt(1)
if n%2 != 0 {
s.Neg(s)
}
t.Sub(t, s)
return t.Div(t, big.NewInt(3))
}

func jacobsthalLucas(n uint) *big.Int {
t := big.NewInt(1)
t.Lsh(t, n)
a := big.NewInt(1)
if n%2 != 0 {
a.Neg(a)
}
}

func main() {
jac := make([]*big.Int, 30)
fmt.Println("First 30 Jacobsthal numbers:")
for i := uint(0); i < 30; i++ {
jac[i] = jacobsthal(i)
fmt.Printf("%9d ", jac[i])
if (i+1)%5 == 0 {
fmt.Println()
}
}

fmt.Println("\nFirst 30 Jacobsthal-Lucas numbers:")
for i := uint(0); i < 30; i++ {
fmt.Printf("%9d ", jacobsthalLucas(i))
if (i+1)%5 == 0 {
fmt.Println()
}
}

fmt.Println("\nFirst 20 Jacobsthal oblong numbers:")
for i := uint(0); i < 20; i++ {
t := big.NewInt(0)
fmt.Printf("%11d ", t.Mul(jac[i], jac[i+1]))
if (i+1)%5 == 0 {
fmt.Println()
}
}

fmt.Println("\nFirst 20 Jacobsthal primes:")
for n, count := uint(0), 0; count < 20; n++ {
j := jacobsthal(n)
if j.ProbablyPrime(10) {
fmt.Println(j)
count++
}
}
}
```
Output:
```First 30 Jacobsthal numbers:
0         1         1         3         5
11        21        43        85       171
341       683      1365      2731      5461
10923     21845     43691     87381    174763
349525    699051   1398101   2796203   5592405
11184811  22369621  44739243  89478485 178956971

First 30 Jacobsthal-Lucas numbers:
2         1         5         7        17
31        65       127       257       511
1025      2047      4097      8191     16385
32767     65537    131071    262145    524287
1048577   2097151   4194305   8388607  16777217
33554431  67108865 134217727 268435457 536870911

First 20 Jacobsthal oblong numbers:
0           1           3          15          55
231         903        3655       14535       58311
232903      932295     3727815    14913991    59650503
238612935   954429895  3817763271 15270965703 61084037575

First 20 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
2932031007403
768614336404564651
201487636602438195784363
845100400152152934331135470251
56713727820156410577229101238628035243
62357403192785191176690552862561408838653121833643
1046183622564446793972631570534611069350392574077339085483
267823007376498379256993682056860433753700498963798805883563
5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443
```

```jacobsthal :: [Integer]
jacobsthal = 0 : 1 : zipWith (\x y -> 2 * x + y) jacobsthal (tail jacobsthal)

jacobsthalLucas :: [Integer]
jacobsthalLucas = 2 : 1 : zipWith (\x y -> 2 * x + y) jacobsthalLucas (tail jacobsthalLucas)

jacobsthalOblong :: [Integer]
jacobsthalOblong = zipWith (*) jacobsthal (tail jacobsthal)

isPrime :: Integer -> Bool
isPrime n = n > 1 && not (or [n `mod` i == 0 | i <- [2 .. floor (sqrt (fromInteger n))]])

main :: IO ()
main = do
putStrLn "First 30 Jacobsthal numbers:"
print \$ take 30 jacobsthal
putStrLn ""
putStrLn "First 30 Jacobsthal-Lucas numbers:"
print \$ take 30 jacobsthalLucas
putStrLn ""
putStrLn "First 20 Jacobsthal oblong numbers:"
print \$ take 20 jacobsthalOblong
putStrLn ""
putStrLn "First 10 Jacobsthal primes:"
print \$ take 10 \$ filter isPrime jacobsthal
```
Output:
```First 30 Jacobsthal numbers:
[0,1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,21845,43691,87381,174763,349525,699051,1398101,2796203,5592405,11184811,22369621,44739243,89478485,178956971]

First 30 Jacobsthal-Lucas numbers:
[2,1,5,7,17,31,65,127,257,511,1025,2047,4097,8191,16385,32767,65537,131071,262145,524287,1048577,2097151,4194305,8388607,16777217,33554431,67108865,134217727,268435457,536870911]

First 20 Jacobsthal oblong numbers:
[0,1,3,15,55,231,903,3655,14535,58311,232903,932295,3727815,14913991,59650503,238612935,954429895,3817763271,15270965703,61084037575]

First 10 Jacobsthal primes:
[3,5,11,43,683,2731,43691,174763,2796203,715827883]
```

or, defined in terms of unfoldr:

```import Data.List (intercalate, transpose, uncons, unfoldr)
import Data.List.Split (chunksOf)
import Data.Numbers.Primes (isPrime)
import Text.Printf (printf)

-------------------- JACOBSTHAL NUMBERS ------------------

jacobsthal :: [Integer]
jacobsthal = jacobsthalish (0, 1)

jacobsthalish :: (Integer, Integer) -> [Integer]
jacobsthalish = unfoldr go
where
go (a, b) = Just (a, (b, 2 * a + b))

--------------------------- TEST -------------------------
main :: IO ()
main =
mapM_
(putStrLn . format)
[ ( "terms of the Jacobsthal sequence",
30,
jacobsthal
),
( "Jacobsthal-Lucas numbers",
30,
jacobsthalish (2, 1)
),
( "Jacobsthal oblong numbers",
20,
zipWith (*) jacobsthal (tail jacobsthal)
),
( "Jacobsthal primes",
10,
filter isPrime jacobsthal
)
]

format :: (String, Int, [Integer]) -> String
format (k, n, xs) =
show n <> (' ' : k) <> ":\n"
<> table
"  "
(chunksOf 5 \$ show <\$> take n xs)

table :: String -> [[String]] -> String
table gap rows =
let ws = maximum . fmap length <\$> transpose rows
pw = printf . flip intercalate ["%", "s"] . show
in unlines \$ intercalate gap . zipWith pw ws <\$> rows
```
Output:
```30 terms of the Jacobsthal sequence:
0         1         1         3          5
11        21        43        85        171
341       683      1365      2731       5461
10923     21845     43691     87381     174763
349525    699051   1398101   2796203    5592405
11184811  22369621  44739243  89478485  178956971

30 Jacobsthal-Lucas numbers:
2         1          5          7         17
31        65        127        257        511
1025      2047       4097       8191      16385
32767     65537     131071     262145     524287
1048577   2097151    4194305    8388607   16777217
33554431  67108865  134217727  268435457  536870911

20 Jacobsthal oblong numbers:
0          1           3           15           55
231        903        3655        14535        58311
232903     932295     3727815     14913991     59650503
238612935  954429895  3817763271  15270965703  61084037575

10 Jacobsthal primes:
3      5      11       43        683
2731  43691  174763  2796203  715827883```

## J

Implementation:

```ja=: 3 %~ 2x&^ - _1x&^ NB. Jacobsthal
jl=:      2x&^ + _1x&^ NB.Jacobsthal-Lucas
```

```   ja i.3 10
0      1       1       3       5       11       21       43       85       171
341    683    1365    2731    5461    10923    21845    43691    87381    174763
349525 699051 1398101 2796203 5592405 11184811 22369621 44739243 89478485 178956971
jl i.3 10
2       1       5       7       17       31       65       127       257       511
1025    2047    4097    8191    16385    32767    65537    131071    262145    524287
1048577 2097151 4194305 8388607 16777217 33554431 67108865 134217727 268435457 536870911
2 10\$2 */\ ja i.21 NB. Jacobsthal oblong
0      1       3       15       55       231       903       3655       14535       58311
232903 932295 3727815 14913991 59650503 238612935 954429895 3817763271 15270965703 61084037575
ja I.1 p:ja i.32  NB. first ten Jacobsthal primes
3 5 11 43 683 2731 43691 174763 2796203 715827883
```

## Java

```import java.math.BigInteger;

public final class JacobsthalNumbers {

public static void main(String[] aArgs) {
System.out.println("The first 30 Jacobsthal Numbers:");
for ( int i = 0; i < 6; i++ ) {
for ( int k = 0; k < 5; k++ ) {
System.out.print(String.format("%15s", jacobsthalNumber(i * 5 + k)));
}
System.out.println();
}
System.out.println();

System.out.println("The first 30 Jacobsthal-Lucas Numbers:");
for ( int i = 0; i < 6; i++ ) {
for ( int k = 0; k < 5; k++ ) {
System.out.print(String.format("%15s", jacobsthalLucasNumber(i * 5 + k)));
}
System.out.println();
}
System.out.println();

System.out.println("The first 20 Jacobsthal oblong Numbers:");
for ( int i = 0; i < 4; i++ ) {
for ( int k = 0; k < 5; k++ ) {
System.out.print(String.format("%15s", jacobsthalOblongNumber(i * 5 + k)));
}
System.out.println();
}
System.out.println();

System.out.println("The first 10 Jacobsthal Primes:");
for ( int i = 0; i < 10; i++ ) {
}
}

private static BigInteger jacobsthalNumber(int aIndex) {
BigInteger value = BigInteger.valueOf(parityValue(aIndex));
return BigInteger.ONE.shiftLeft(aIndex).subtract(value).divide(THREE);
}

private static long jacobsthalLucasNumber(int aIndex) {
return ( 1 << aIndex ) + parityValue(aIndex);
}

private static long jacobsthalOblongNumber(int aIndex) {
long nextJacobsthal =  jacobsthalNumber(aIndex + 1).longValueExact();
long result = currentJacobsthal * nextJacobsthal;
currentJacobsthal = nextJacobsthal;
return result;
}

private static long jacobsthalPrimeNumber(int aIndex) {
BigInteger candidate = jacobsthalNumber(latestIndex++);
while ( ! candidate.isProbablePrime(CERTAINTY) ) {
candidate = jacobsthalNumber(latestIndex++);
}
return candidate.longValueExact();
}

private static int parityValue(int aIndex) {
return ( aIndex & 1 ) == 0 ? +1 : -1;
}

private static long currentJacobsthal = 0;
private static int latestIndex = 0;

private static final BigInteger THREE = BigInteger.valueOf(3);
private static final int CERTAINTY = 20;
}
```
Output:
```The first 30 Jacobsthal Numbers:
0              1              1              3              5
11             21             43             85            171
341            683           1365           2731           5461
10923          21845          43691          87381         174763
349525         699051        1398101        2796203        5592405
11184811       22369621       44739243       89478485      178956971

The first 30 Jacobsthal-Lucas Numbers:
2              1              5              7             17
31             65            127            257            511
1025           2047           4097           8191          16385
32767          65537         131071         262145         524287
1048577        2097151        4194305        8388607       16777217
33554431       67108865      134217727      268435457      536870911

The first 20 Jacobsthal oblong Numbers:
0              1              3             15             55
231            903           3655          14535          58311
232903         932295        3727815       14913991       59650503
238612935      954429895     3817763271    15270965703    61084037575

The first 10 Jacobsthal Primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
```

## jq

Works with gojq, the Go implementation of jq

See Erdős-primes#jq for a suitable definition of `is_prime` as used here. As a practical matter, this function limits the exploration of Jacobsthal primes.

Preliminaries

```# Split the input array into a stream of arrays
def chunks(n):
def c: .[0:n], (if length > n then .[n:]|c else empty end);
c;

def lpad(\$len): tostring | (\$len - length) as \$l | (" " * \$l)[:\$l] + .;

# If \$j is 0, then an error condition is raised;
# otherwise, assuming infinite-precision integer arithmetic,
# if the input and \$j are integers, then the result will be a pair of integers.
def divmod(\$j):
. as \$i
| (\$i % \$j) as \$mod
| [(\$i - \$mod) / \$j, \$mod] ;

# To take advantage of gojq's arbitrary-precision integer arithmetic:
def power(\$b): . as \$in | reduce range(0;\$b) as \$i (1; . * \$in);```

```def jacobsthal:
. as \$n
| ( (2|power(\$n)) - (if (\$n%2 == 0) then 1 else -1 end)) | divmod(3)[0];

def jacobsthalLucas:
. as \$n
| (2|power(\$n)) + (if (\$n%2 == 0) then 1 else -1 end);

def pp(\$width): chunks(5) | map(lpad(\$width)) | join("");

[range(0;30) | jacobsthal] as \$js
| "First 30 Jacobsthal numbers:",
( \$js | pp(12)),

"\nFirst 30 Jacobsthal-Lucas numbers:",
( [range(0;30) | jacobsthalLucas]  | pp(12)),

"\nFirst 20 Jacobsthal oblong numbers:",
( [range(0;20) | \$js[.] * \$js[1+.]] | pp(14)),

"\nFirst 11 Jacobsthal primes:",
limit(11; range(0; infinite) | jacobsthal | select(is_prime))
;

Output:
```First 30 Jacobsthal numbers:
0           1           1           3           5
11          21          43          85         171
341         683        1365        2731        5461
10923       21845       43691       87381      174763
349525      699051     1398101     2796203     5592405
11184811    22369621    44739243    89478485   178956971

First 30 Jacobsthal-Lucas numbers:
2           1           5           7          17
31          65         127         257         511
1025        2047        4097        8191       16385
32767       65537      131071      262145      524287
1048577     2097151     4194305     8388607    16777217
33554431    67108865   134217727   268435457   536870911

First 20 Jacobsthal oblong numbers:
0             1             3            15            55
231           903          3655         14535         58311
232903        932295       3727815      14913991      59650503
238612935     954429895    3817763271   15270965703   61084037575

First 11 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
2932031007403
```

## Julia

```using Lazy
using Primes

J(n) = (2^n - (-1)^n) ÷ 3
L(n) =  2^n + (-1)^n

Jacobsthal = @>> Lazy.range(0) map(J)
JLucas = @>> Lazy.range(0) map(L)
Joblong = @>> Lazy.range(big"0") map(n -> J(n) * J(n + 1))
Jprimes = @>> Lazy.range(big"0") map(J) filter(isprime)

function printrows(title, vec, columnsize = 15, columns = 5, rjust=true)
println(title)
for (i, n) in enumerate(vec)
print((rjust ? lpad : rpad)(n, columnsize), i % columns == 0 ? "\n" : "")
end
println()
end

printrows("Thirty Jacobsthal numbers:", collect(take(30, Jacobsthal)))
printrows("Thirty Jacobsthal-Lucas numbers:", collect(take(30, JLucas)))
printrows("Twenty oblong Jacobsthal numbers:", collect(take(20, Joblong)))
printrows("Fifteen Jacabsthal prime numbers:", collect(take(15, Jprimes)), 40, 1, false)
```
Output:
```Thirty Jacobsthal numbers:
0              1              1              3              5
11             21             43             85            171
341            683           1365           2731           5461
10923          21845          43691          87381         174763
349525         699051        1398101        2796203        5592405
11184811       22369621       44739243       89478485      178956971

Thirty Jacobsthal-Lucas numbers:
2              1              5              7             17
31             65            127            257            511
1025           2047           4097           8191          16385
32767          65537         131071         262145         524287
1048577        2097151        4194305        8388607       16777217
33554431       67108865      134217727      268435457      536870911

Twenty oblong Jacobsthal numbers:
0              1              3             15             55
231            903           3655          14535          58311
232903         932295        3727815       14913991       59650503
238612935      954429895     3817763271    15270965703    61084037575

Fifteen Jacabsthal prime numbers:
3
5
11
43
683
2731
43691
174763
2796203
715827883
2932031007403
768614336404564651
201487636602438195784363
845100400152152934331135470251
56713727820156410577229101238628035243
```

## Mathematica/Wolfram Language

```ClearAll[Jacobsthal, JacobsthalLucas, JacobsthalOblong]
Jacobsthal[n_]:=(2^n-(-1)^n)/3
JacobsthalLucas[n_]:=2^n+(-1)^n
JacobsthalOblong[n_]:=Jacobsthal[n]Jacobsthal[n+1]
Jacobsthal[Range[0, 29]]
JacobsthalLucas[Range[0, 29]]
JacobsthalOblong[Range[0, 19]]
n=0;
i=0;
Reap[While[n<20,
If[
PrimeQ[Jacobsthal[i]]
,
Sow[{i,Jacobsthal[i]}];
n++;
];
i++;
]][[2,1]]//Grid
```
Output:
```{0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763, 349525, 699051, 1398101, 2796203, 5592405, 11184811, 22369621, 44739243, 89478485, 178956971}

{2, 1, 5, 7, 17, 31, 65, 127, 257, 511, 1025, 2047, 4097, 8191, 16385, 32767, 65537, 131071, 262145, 524287, 1048577, 2097151, 4194305, 8388607, 16777217, 33554431, 67108865, 134217727, 268435457, 536870911}

{0, 1, 3, 15, 55, 231, 903, 3655, 14535, 58311, 232903, 932295, 3727815, 14913991, 59650503, 238612935, 954429895, 3817763271, 15270965703, 61084037575}

3	3
4	5
5	11
7	43
11	683
13	2731
17	43691
19	174763
23	2796203
31	715827883
43	2932031007403
61	768614336404564651
79	201487636602438195784363
101	845100400152152934331135470251
127	56713727820156410577229101238628035243
167	62357403192785191176690552862561408838653121833643
191	1046183622564446793972631570534611069350392574077339085483
199	267823007376498379256993682056860433753700498963798805883563
313	5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
347	95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443```

## Maxima

```jacobstahl(n):=(2^n-(-1)^n)/3\$

jacobstahl_lucas(n):=2^n+(-1)^n\$

jacobstahl_oblong(n):=jacobstahl(n)*jacobstahl(n+1)\$

/* Function that returns a list of the first len jacobstahl primes */
jacobstahl_primes_count(len):=block(
[i:0,count:0,result:[]],
while count<len do (if primep(jacobstahl(i)) then (result:endcons(jacobstahl(i),result),count:count+1),i:i+1),
result)\$

/* Test cases */
makelist(jacobstahl(i),i,0,29);
makelist(jacobstahl_lucas(i),i,0,29);
makelist(jacobstahl_oblong(i),i,0,19);
jacobstahl_primes_count(10);
```
Output:
```[0,1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,21845,43691,87381,174763,349525,699051,1398101,2796203,5592405,11184811,22369621,44739243,89478485,178956971]
[2,1,5,7,17,31,65,127,257,511,1025,2047,4097,8191,16385,32767,65537,131071,262145,524287,1048577,2097151,4194305,8388607,16777217,33554431,67108865,134217727,268435457,536870911]
[0,1,3,15,55,231,903,3655,14535,58311,232903,932295,3727815,14913991,59650503,238612935,954429895,3817763271,15270965703,61084037575]

[3,5,11,43,683,2731,43691,174763,2796203,715827883]
```

## Nim

```import std/strutils

func isPrime(n: Natural): bool =
## Return true if "n" is prime.
if n < 2: return false
if n mod 2 == 0: return n == 2
if n mod 3 == 0: return n == 3
var step = 2
var d = 5
while d * d <= n:
if n mod d == 0: return false
inc d, step
step = 6 - step
result = true

iterator jacobsthalSequence(first, second: int): int =
## Yield the successive Jacobsthal numbers or
## Jacobsthal-Lucas numbers.
var prev = first
var curr = second
yield prev
yield curr
while true:
swap prev, curr
curr += curr + prev
yield curr

iterator jacobsthalOblong(): int =
## Yield the successive Jacobsthal oblong numbers.
var prev = -1
for n in jacobsthalSequence(0, 1):
if prev >= 0:
yield prev * n
prev = n

iterator jacobsthalPrimes(): int =
## Yield the successive Jacobsthal prime numbers.
for n in jacobsthalSequence(0, 1):
if n.isPrime:
yield n

echo "First 30 Jacobsthal numbers:"
var count = 0
for n in jacobsthalSequence(0, 1):
inc count
stdout.write align(\$n, 11)
if count mod 6 == 0: echo()
if count == 30: break

echo "\nFirst 30 Jacobsthal-Lucas numbers:"
count = 0
for n in jacobsthalSequence(2, 1):
inc count
stdout.write align(\$n, 11)
if count mod 6 == 0: echo()
if count == 30: break

echo "\nFirst 20 Jacobsthal oblong numbers:"
count = 0
for n in jacobsthalOblong():
inc count
stdout.write align(\$n, 13)
if count mod 5 == 0: echo()
if count == 20: break

echo "\nFirst 10 Jacobsthal prime numbers:"
count = 0
for n in jacobsthalPrimes():
inc count
stdout.write align(\$n, 11)
if count mod 5 == 0: echo()
if count == 10: break
```
Output:
```First 30 Jacobsthal numbers:
0          1          1          3          5         11
21         43         85        171        341        683
1365       2731       5461      10923      21845      43691
87381     174763     349525     699051    1398101    2796203
5592405   11184811   22369621   44739243   89478485  178956971

First 30 Jacobsthal-Lucas numbers:
2          1          5          7         17         31
65        127        257        511       1025       2047
4097       8191      16385      32767      65537     131071
262145     524287    1048577    2097151    4194305    8388607
16777217   33554431   67108865  134217727  268435457  536870911

First 20 Jacobsthal oblong numbers:
0            1            3           15           55
231          903         3655        14535        58311
232903       932295      3727815     14913991     59650503
238612935    954429895   3817763271  15270965703  61084037575

First 10 Jacobsthal prime numbers:
3          5         11         43        683
2731      43691     174763    2796203  715827883
```

## OCaml

```let is_prime n =
let rec test x =
x * x > n || n mod x <> 0 && n mod (x + 2) <> 0 && test (x + 6)
in
if n < 5
then n land 2 <> 0
else n land 1 <> 0 && n mod 3 <> 0 && test 5

let seq_jacobsthal =
let rec next b a () = Seq.Cons (a, next (a + a + b) b) in
next 1

let seq_jacobsthal_oblong =
let rec next b a () = Seq.Cons (a * b, next (a + a + b) b) in
next 1 0

let () =
let show (n, seq, s) =
Seq.take n seq
|> Seq.fold_left (Printf.sprintf "%s %u") (Printf.sprintf "First %u %s numbers:\n" n s)
|> print_endline
in
List.iter show [
30, seq_jacobsthal 0, "Jacobsthal";
30, seq_jacobsthal 2, "Jacobsthal-Lucas";
20, seq_jacobsthal_oblong, "Jacobsthal oblong";
10, Seq.filter is_prime (seq_jacobsthal 0), "Jacobsthal prime"]
```
Output:
```First 30 Jacobsthal numbers:
0 1 1 3 5 11 21 43 85 171 341 683 1365 2731 5461 10923 21845 43691 87381 174763 349525 699051 1398101 2796203 5592405 11184811 22369621 44739243 89478485 178956971
First 30 Jacobsthal-Lucas numbers:
2 1 5 7 17 31 65 127 257 511 1025 2047 4097 8191 16385 32767 65537 131071 262145 524287 1048577 2097151 4194305 8388607 16777217 33554431 67108865 134217727 268435457 536870911
First 20 Jacobsthal oblong numbers:
0 1 3 15 55 231 903 3655 14535 58311 232903 932295 3727815 14913991 59650503 238612935 954429895 3817763271 15270965703 61084037575
First 10 Jacobsthal prime numbers:
3 5 11 43 683 2731 43691 174763 2796203 715827883
```

## PARI/GP

```\\ Define the Jacobsthal function
Jacobsthal(n) = (2^n - (-1)^n) / 3;

\\ Define the JacobsthalLucas function
JacobsthalLucas(n) = 2^n + (-1)^n;

\\ Define the JacobsthalOblong function
JacobsthalOblong(n) = Jacobsthal(n) * Jacobsthal(n + 1);

{
\\ Generate and print Jacobsthal numbers for 0 through 29
print(vector(30, n, Jacobsthal(n-1)));

\\ Generate and print JacobsthalLucas numbers for 0 through 29
print(vector(30, n, JacobsthalLucas(n-1)));

\\ Generate and print JacobsthalOblong numbers for 0 through 19
print(vector(20, n, JacobsthalOblong(n-1)));

\\ Find the first 20 prime numbers in the Jacobsthal sequence
myprimes = [];
i = 0;
while(#myprimes < 40,
if(isprime(Jacobsthal(i)), myprimes = concat(myprimes, [i, Jacobsthal(i)]));
i++;
);

for (i = 1, #myprimes\2,      print(myprimes[2*i-1] "	" myprimes[2*i]); );
}```
Output:
```[0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763, 349525, 699051, 1398101, 2796203, 5592405, 11184811, 22369621, 44739243, 89478485, 178956971]
[2, 1, 5, 7, 17, 31, 65, 127, 257, 511, 1025, 2047, 4097, 8191, 16385, 32767, 65537, 131071, 262145, 524287, 1048577, 2097151, 4194305, 8388607, 16777217, 33554431, 67108865, 134217727, 268435457, 536870911]
[0, 1, 3, 15, 55, 231, 903, 3655, 14535, 58311, 232903, 932295, 3727815, 14913991, 59650503, 238612935, 954429895, 3817763271, 15270965703, 61084037575]
3	3
4	5
5	11
7	43
11	683
13	2731
17	43691
19	174763
23	2796203
31	715827883
43	2932031007403
61	768614336404564651
79	201487636602438195784363
101	845100400152152934331135470251
127	56713727820156410577229101238628035243
167	62357403192785191176690552862561408838653121833643
191	1046183622564446793972631570534611069350392574077339085483
199	267823007376498379256993682056860433753700498963798805883563
313	5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
347	95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443

```

## Perl

Library: ntheory
```use strict;
use warnings;
use feature <say state>;
use bigint;
use List::Util 'max';
use ntheory 'is_prime';

sub table { my \$t = 5 * (my \$c = 1 + length max @_); ( sprintf( ('%'.\$c.'d')x@_, @_) ) =~ s/.{1,\$t}\K/\n/gr }

sub jacobsthal       { my(\$n) = @_; state  @J = (0, 1); do { push  @J,  \$J[-1] + 2 *  \$J[-2]} until  @J > \$n;  \$J[\$n] }
sub jacobsthal_lucas { my(\$n) = @_; state @JL = (2, 1); do { push @JL, \$JL[-1] + 2 * \$JL[-2]} until @JL > \$n; \$JL[\$n] }

my(@j,@jp,\$c,\$n);
push @j, jacobsthal \$_ for 0..29;
do { is_prime(\$n = ( 2**++\$c - -1**\$c ) / 3) and push @jp, \$n } until @jp == 20;

say "First 30 Jacobsthal numbers:\n",        table @j;
say "First 30 Jacobsthal-Lucas numbers:\n",  table map { jacobsthal_lucas \$_-1 } 1..30;
say "First 20 Jacobsthal oblong numbers:\n", table map { \$j[\$_-1] * \$j[\$_]     } 1..20;
say "First 20 Jacobsthal primes:\n",         join "\n", @jp;
```
Output:
```First 30 Jacobsthal numbers:
0         1         1         3         5
11        21        43        85       171
341       683      1365      2731      5461
10923     21845     43691     87381    174763
349525    699051   1398101   2796203   5592405
11184811  22369621  44739243  89478485 178956971

First 30 Jacobsthal-Lucas numbers:
2         1         5         7        17
31        65       127       257       511
1025      2047      4097      8191     16385
32767     65537    131071    262145    524287
1048577   2097151   4194305   8388607  16777217
33554431  67108865 134217727 268435457 536870911

First 20 Jacobsthal oblong numbers:
0           1           3          15          55
231         903        3655       14535       58311
232903      932295     3727815    14913991    59650503
238612935   954429895  3817763271 15270965703 61084037575

First 20 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
2932031007403
768614336404564651
201487636602438195784363
845100400152152934331135470251
56713727820156410577229101238628035243
62357403192785191176690552862561408838653121833643
1046183622564446793972631570534611069350392574077339085483
267823007376498379256993682056860433753700498963798805883563
5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443```

## Phix

You can run this online here.

```with javascript_semantics
function jacobsthal(integer n)
return floor((power(2,n)+odd(n))/3)
end function

function jacobsthal_lucas(integer n)
return power(2,n)+power(-1,n)
end function

function jacobsthal_oblong(integer n)
return jacobsthal(n)*jacobsthal(n+1)
end function

function jba(string fmt, sequence s, integer b=5)
return {join_by(apply(true,sprintf,{{fmt},s}),1,b," ")}
end function
printf(1,"First 30 Jacobsthal numbers:\n%s\n",       jba("%9d",apply(tagset(29,0),jacobsthal)))
printf(1,"First 30 Jacobsthal-Lucas numbers:\n%s\n", jba("%9d",apply(tagset(29,0),jacobsthal_lucas)))
printf(1,"First 20 Jacobsthal oblong numbers:\n%s\n",jba("%11d",apply(tagset(19,0),jacobsthal_oblong)))
--printf(1,"First 10 Jacobsthal primes:\n%s\n", jba("%d",filter(apply(tagset(31,0),jacobsthal),is_prime),1))
--hmm(""), fine, but to go further roll out gmp:
include mpfr.e
mpz z = mpz_init()
integer n = 1, found = 0
printf(1,"First 20 jacobsthal primes:\n")
while found<20 do
mpz_ui_pow_ui(z,2,n)
{} = mpz_fdiv_q_ui(z,z,3)
if mpz_prime(z) then
found += 1
printf(1,"%s\n",{mpz_get_str(z)})
end if
n += 1
end while
```

Likewise should you want the three basic functions to go further they'll have to look much more like the C submission above.

Output:
```First 30 Jacobsthal numbers:
0         1         1         3         5
11        21        43        85       171
341       683      1365      2731      5461
10923     21845     43691     87381    174763
349525    699051   1398101   2796203   5592405
11184811  22369621  44739243  89478485 178956971

First 30 Jacobsthal-Lucas numbers:
2         1         5         7        17
31        65       127       257       511
1025      2047      4097      8191     16385
32767     65537    131071    262145    524287
1048577   2097151   4194305   8388607  16777217
33554431  67108865 134217727 268435457 536870911

First 20 Jacobsthal oblong numbers:
0           1           3          15          55
231         903        3655       14535       58311
232903      932295     3727815    14913991    59650503
238612935   954429895  3817763271 15270965703 61084037575

First 20 jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
2932031007403
768614336404564651
201487636602438195784363
845100400152152934331135470251
56713727820156410577229101238628035243
62357403192785191176690552862561408838653121833643
1046183622564446793972631570534611069350392574077339085483
267823007376498379256993682056860433753700498963798805883563
5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443
```

## Python

Translation of: Phix
```#!/usr/bin/python
from math import floor, pow

def isPrime(n):
for i in range(2, int(n**0.5) + 1):
if n % i == 0:
return False
return True

def odd(n):
return n and 1 != 0

def jacobsthal(n):
return floor((pow(2,n)+odd(n))/3)

def jacobsthal_lucas(n):
return int(pow(2,n)+pow(-1,n))

def jacobsthal_oblong(n):
return jacobsthal(n)*jacobsthal(n+1)

if __name__ == '__main__':
print("First 30 Jacobsthal numbers:")
for j in range(0, 30):
print(jacobsthal(j), end="  ")

print("\n\nFirst 30 Jacobsthal-Lucas numbers: ")
for j in range(0, 30):
print(jacobsthal_lucas(j), end = '\t')

print("\n\nFirst 20 Jacobsthal oblong numbers: ")
for j in range(0, 20):
print(jacobsthal_oblong(j), end="  ")

print("\n\nFirst 10 Jacobsthal primes: ")
for j in range(3, 33):
if isPrime(jacobsthal(j)):
print(jacobsthal(j))
```
Output:
```First 30 Jacobsthal numbers:
0  1  1  3  5  11  21  43  85  171  341  683  1365  2731  5461  10923  21845  43691  87381  174763  349525  699051  1398101  2796203  5592405  11184811  22369621  44739243  89478485  178956971

First 30 Jacobsthal-Lucas numbers:
2	1	5	7	17	31	65	127	257	511	1025	2047	4097	8191	16385	32767	65537	131071	262145	524287	1048577	2097151	4194305	8388607	16777217	33554431	67108865	134217727	268435457	536870911

First 20 Jacobsthal oblong numbers:
0  1  3  15  55  231  903  3655  14535  58311  232903  932295  3727815  14913991  59650503  238612935  954429895  3817763271  15270965703  61084037575

First 10 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883```

Or, defining an infinite series in terms of a general unfoldr anamorphism:

```'''Jacobsthal numbers'''

from itertools import islice
from operator import mul

# jacobsthal :: [Integer]
def jacobsthal():
'''Infinite sequence of terms of OEIS A001045
'''
return jacobsthalish(0, 1)

# jacobsthalish :: (Int, Int) -> [Int]
def jacobsthalish(*xy):
'''Infinite sequence of jacobsthal-type series
beginning with a, b
'''
def go(ab):
a, b = ab
return a, (b, 2 * a + b)

return unfoldr(go)(xy)

# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''First 15 terms each n-step Fibonacci(n) series
where n is drawn from [2..8]
'''
print('\n\n'.join([
fShow(*x) for x in [
(
'terms of the Jacobsthal sequence',
30, jacobsthal()),
(
'Jacobsthal-Lucas numbers',
30, jacobsthalish(2, 1)
),
(
'Jacobsthal oblong numbers',
20, map(
mul, jacobsthal(),
drop(1)(jacobsthal())
)
),
(
'primes in the Jacobsthal sequence',
10, filter(isPrime, jacobsthal())
)
]
]))

# fShow :: (String, Int, [Integer]) -> String
def fShow(k, n, xs):
'''N tabulated terms of XS, prefixed by the label K
'''
return f'{n} {k}:\n' + spacedTable(
list(chunksOf(5)(
[str(t) for t in take(n)(xs)]
))
)

# ----------------------- GENERIC ------------------------

# drop :: Int -> [a] -> [a]
# drop :: Int -> String -> String
def drop(n):
'''The sublist of xs beginning at
(zero-based) index n.
'''
def go(xs):
if isinstance(xs, (list, tuple, str)):
return xs[n:]
else:
take(n)(xs)
return xs
return go

# isPrime :: Int -> Bool
def isPrime(n):
'''True if n is prime.'''
if n in (2, 3):
return True
if 2 > n or 0 == n % 2:
return False
if 9 > n:
return True
if 0 == n % 3:
return False

def p(x):
return 0 == n % x or 0 == n % (2 + x)

return not any(map(p, range(5, 1 + int(n ** 0.5), 6)))

# take :: Int -> [a] -> [a]
# take :: Int -> String -> String
def take(n):
'''The prefix of xs of length n,
or xs itself if n > length xs.
'''
def go(xs):
return (
xs[0:n]
if isinstance(xs, (list, tuple))
else list(islice(xs, n))
)
return go

# unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
def unfoldr(f):
'''Generic anamorphism.
A lazy (generator) list unfolded from a seed value by
repeated application of f until no residue remains.
Dual to fold/reduce.
f returns either None, or just (value, residue).
For a strict output value, wrap in list().
'''
def go(x):
valueResidue = f(x)
while None is not valueResidue:
yield valueResidue[0]
valueResidue = f(valueResidue[1])
return go

# ---------------------- FORMATTING ----------------------

# chunksOf :: Int -> [a] -> [[a]]
def chunksOf(n):
'''A series of lists of length n, subdividing the
contents of xs. Where the length of xs is not evenly
divisible, the final list will be shorter than n.
'''
def go(xs):
return (
xs[i:n + i] for i in range(0, len(xs), n)
) if 0 < n else None
return go

# spacedTable :: [[String]] -> String
def spacedTable(rows):
'''Tabulated stringification of rows'''
columnWidths = [
max([len(x) for x in col])
for col in zip(*rows)
]
return '\n'.join([
' '.join(
map(
lambda x, w: x.rjust(w, ' '),
row, columnWidths
)
)
for row in rows
])

# MAIN ---
if __name__ == '__main__':
main()
```
Output:
```30 terms of the Jacobsthal sequence:
0        1        1        3         5
11       21       43       85       171
341      683     1365     2731      5461
10923    21845    43691    87381    174763
349525   699051  1398101  2796203   5592405
11184811 22369621 44739243 89478485 178956971

30 Jacobsthal-Lucas numbers:
2        1         5         7        17
31       65       127       257       511
1025     2047      4097      8191     16385
32767    65537    131071    262145    524287
1048577  2097151   4194305   8388607  16777217
33554431 67108865 134217727 268435457 536870911

20 Jacobsthal oblong numbers:
0         1          3          15          55
231       903       3655       14535       58311
232903    932295    3727815    14913991    59650503
238612935 954429895 3817763271 15270965703 61084037575

10 primes in the Jacobsthal sequence:
3     5     11      43       683
2731 43691 174763 2796203 715827883```

## Quackery

`isprime` is defined at Primality by trial division#Quackery.

```  [ 2 over ** -1 rot ** - 3 / ] is j  ( n --> n )

[ 2 over ** -1 rot ** + ]     is jl ( n --> n )

[ dup 1+ j swap j * ]         is jo ( n --> n )

say "First 30 Jacobsthal numbers:"
cr
30 times [ i^ j echo sp ]
cr cr
say "First 30 Jacobsthal-Lucas numbers:"
cr
30 times [ i^ jl echo sp ]
cr cr
say "First 20 Jacobsthal oblong numbers:"
cr
20 times [ i^ jo echo sp ]
cr cr
say "First 10 Jacobsthal primes:"
cr
[] 0
[ dup j dup isprime iff
[ swap dip join ]
else drop
1+
over size 10 = until ]
drop
witheach [ echo sp ]```
Output:
```First 30 Jacobsthal numbers:
0 1 1 3 5 11 21 43 85 171 341 683 1365 2731 5461 10923 21845 43691 87381 174763 349525 699051 1398101 2796203 5592405 11184811 22369621 44739243 89478485 178956971

First 30 Jacobsthal-Lucas numbers:
2 1 5 7 17 31 65 127 257 511 1025 2047 4097 8191 16385 32767 65537 131071 262145 524287 1048577 2097151 4194305 8388607 16777217 33554431 67108865 134217727 268435457 536870911

First 20 Jacobsthal oblong numbers:
0 1 3 15 55 231 903 3655 14535 58311 232903 932295 3727815 14913991 59650503 238612935 954429895 3817763271 15270965703 61084037575

First 10 Jacobsthal primes:
3 5 11 43 683 2731 43691 174763 2796203 715827883
```

## Raku

```my \$jacobsthal = cache lazy 0, 1, * × 2 + * … *;
my \$jacobsthal-lucas = lazy 2, 1, * × 2 + * … *;

say "First 30 Jacobsthal numbers:";
say \$jacobsthal[^30].batch(5)».fmt("%9d").join: "\n";

say "\nFirst 30 Jacobsthal-Lucas numbers:";
say \$jacobsthal-lucas[^30].batch(5)».fmt("%9d").join: "\n";

say "\nFirst 20 Jacobsthal oblong numbers:";
say (^∞).map( { \$jacobsthal[\$_] × \$jacobsthal[\$_+1] } )[^20].batch(5)».fmt("%11d").join: "\n";

say "\nFirst 20 Jacobsthal primes:";
say \$jacobsthal.grep( &is-prime )[^20].join: "\n";
```
Output:
```First 30 Jacobsthal numbers:
0         1         1         3         5
11        21        43        85       171
341       683      1365      2731      5461
10923     21845     43691     87381    174763
349525    699051   1398101   2796203   5592405
11184811  22369621  44739243  89478485 178956971

First 30 Jacobsthal-Lucas numbers:
2         1         5         7        17
31        65       127       257       511
1025      2047      4097      8191     16385
32767     65537    131071    262145    524287
1048577   2097151   4194305   8388607  16777217
33554431  67108865 134217727 268435457 536870911

First 20 Jacobsthal oblong numbers:
0           1           3          15          55
231         903        3655       14535       58311
232903      932295     3727815    14913991    59650503
238612935   954429895  3817763271 15270965703 61084037575

First 20 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
2932031007403
768614336404564651
201487636602438195784363
845100400152152934331135470251
56713727820156410577229101238628035243
62357403192785191176690552862561408838653121833643
1046183622564446793972631570534611069350392574077339085483
267823007376498379256993682056860433753700498963798805883563
5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443```

## Red

```Red ["Jacobsthal numbers"]

jacobsthal: function [n] [to-integer (2 ** n - (-1 ** n) / 3)]

lucas: function [n] [2 ** n + (-1 ** n)]

oblong: function [n] [
first split mold multiply to-float jacobsthal n to-float jacobsthal n + 1 #"."   ; work around integer overflow
]

prime?: function [
"Returns true if the input is a prime number"
n [number!] "An integer to check for primality"
][
if 2 = n [return true]
if any [1 = n even? n] [return false]
limit: sqrt n
candidate: 3
while [candidate < limit][
if n % candidate = 0 [return false]
candidate: candidate + 2
]
true
]

show: function [n fn][
cols: length? mold fn n
repeat i n [
prin [pad fn subtract i 1 cols]
if i % 5 = 0 [prin newline]
]
prin newline
]

print "First 30 Jacobsthal numbers:"
show 30 :jacobsthal

print "First 30 Jacobsthal-Lucas numbers:"
show 30 :lucas

print "First 20 Jacobsthal oblong numbers:"
show 20 :oblong

print "First 10 Jacobsthal primes:"
primes: n: 0
while [primes < 10][
if prime? jacobsthal n [
print jacobsthal n
primes: primes + 1
]
n: n + 1
]
```
Output:
```First 30 Jacobsthal numbers:
0        1        1        3        5
11       21       43       85       171
341      683      1365     2731     5461
10923    21845    43691    87381    174763
349525   699051   1398101  2796203  5592405
11184811 22369621 44739243 89478485 178956971

First 30 Jacobsthal-Lucas numbers:
2         1         5         7         17
31        65        127       257       511
1025      2047      4097      8191      16385
32767     65537     131071    262145    524287
1048577   2097151   4194305   8388607   16777217
33554431  67108865  134217727 268435457 536870911

First 20 Jacobsthal oblong numbers:
0             1             3             15            55
231           903           3655          14535         58311
232903        932295        3727815       14913991      59650503
238612935     954429895     3817763271    15270965703   61084037575

First 10 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
```

## RPL

### Straightforward approach

The Jacobstahl pieces of code are macros more than programs.

```≪ 2 OVER ^ -1 ROT ^ - 3 / ≫
'JCBN' STO

≪ 2 OVER ^ -1 ROT ^ + ≫
'JCBL' STO

≪ DUP JCBN SWAP 1 + JCBN * ≫
'JCBO' STO
```

The primality test is the only one that deserves such a name:

```≪ IF DUP 5 ≤ THEN
{ 2 3 5 } SWAP POS
ELSE
IF DUP 2 MOD NOT THEN
2
ELSE
DUP √ CEIL → lim
≪ 3
WHILE DUP2 MOD OVER lim ≤ AND REPEAT 2 + END
≫
END
MOD
END
SIGN
≫
'PRIM?' STO
```

### Using binary integers

The task is an opportunity to showcase the use of binary integers in RPL, but it's actually slower and fatter, as many RPL instructions are designed for floating point numbers only.

```≪  → n
≪ # 1h 1 n START SL NEXT
IF n R→B # 1h AND B→R THEN 1 + ELSE 1 - END
3 / B→R
≫ ≫
'JCBN' STO
```

### Testing program

```≪ → func count
≪ { } 0
DO DUP func
IF EVAL THEN ROT SWAP + SWAP ELSE DROP END
1 +
UNTIL OVER SIZE count ≥ END
DROP
≫ ≫
'ASSRT' STO
```
```≪ JCBN 1 ≫ 30 ASSRT
≪ JCBL 1 ≫ 30 ASSRT
≪ JCBO 1 ≫ 20 ASSRT
≪ DUP JCBN PRIM? ≫ 10 ASSRT
```
Works with: Halcyon Calc version 4.2.7
Output:
```4: { 0 1 1 3 5 11 21 43 85 171 341 683 1365 2731 5461 10923 21845 43691 87381 174763 349525 699051 1398101 2796203 5592405 11184811 22369621 44739243 89478485 178956971 }
3: { 2 1 5 7 17 31 65 127 257 511 1025 2047 4097 8191 16385 32767 65537 131071 262145 524287 1048577 2097151 4194305 8388607 16777217 33554431 67108865 134217727 268435457 536870911 }
2: { 0 1 3 15 55 231 903 3655 14535 58311 232903 932295 3727815 14913991 59650503 238612935 954429895 3817763271 15270965703 61084037575 }
1: { 3 5 11 43 683 2731 43691 174763 2796203 715827883 }
```

## Ruby

Since version 3.0, Ruby supports "end-less" method definitions.

```require 'prime'

def jacobsthal(n) = (2**n + n[0])/3
def jacobsthal_lucas(n) = 2**n + (-1)**n
def jacobsthal_oblong(n) = jacobsthal(n) * jacobsthal(n+1)

puts "First 30 Jacobsthal numbers:"
puts (0..29).map{|n| jacobsthal(n) }.join(" ")

puts "\nFirst 30 Jacobsthal-Lucas numbers: "
puts (0..29).map{|n| jacobsthal_lucas(n) }.join(" ")

puts "\nFirst 20 Jacobsthal-Oblong numbers: "
puts (0..19).map{|n| jacobsthal_oblong(n) }.join(" ")

puts "\nFirst 10 prime Jacobsthal numbers: "
res = (0..).lazy.filter_map do |i|
j = jacobsthal(i)
j if j.prime?
end
puts res.take(10).force.join(" ")
```
Output:
```First 30 Jacobsthal numbers:
0 1 1 3 5 11 21 43 85 171 341 683 1365 2731 5461 10923 21845 43691 87381 174763 349525 699051 1398101 2796203 5592405 11184811 22369621 44739243 89478485 178956971

First 30 Jacobsthal-Lucas numbers:
2 1 5 7 17 31 65 127 257 511 1025 2047 4097 8191 16385 32767 65537 131071 262145 524287 1048577 2097151 4194305 8388607 16777217 33554431 67108865 134217727 268435457 536870911

First 20 Jacobsthal-Oblong numbers:
0 1 3 15 55 231 903 3655 14535 58311 232903 932295 3727815 14913991 59650503 238612935 954429895 3817763271 15270965703 61084037575

First 10 prime Jacobsthal numbers:
3 5 11 43 683 2731 43691 174763 2796203 715827883
```

## Rust

```// [dependencies]
// rug = "0.3"

use rug::integer::IsPrime;
use rug::Integer;

fn jacobsthal_numbers() -> impl std::iter::Iterator<Item = Integer> {
(0..).map(|x| ((Integer::from(1) << x) - if x % 2 == 0 { 1 } else { -1 }) / 3)
}

fn jacobsthal_lucas_numbers() -> impl std::iter::Iterator<Item = Integer> {
(0..).map(|x| (Integer::from(1) << x) + if x % 2 == 0 { 1 } else { -1 })
}

fn jacobsthal_oblong_numbers() -> impl std::iter::Iterator<Item = Integer> {
let mut jn = jacobsthal_numbers();
let mut n0 = jn.next().unwrap();
std::iter::from_fn(move || {
let n1 = jn.next().unwrap();
let result = Integer::from(&n0 * &n1);
n0 = n1;
Some(result)
})
}

fn jacobsthal_primes() -> impl std::iter::Iterator<Item = Integer> {
jacobsthal_numbers().filter(|x| x.is_probably_prime(30) != IsPrime::No)
}

fn main() {
println!("First 30 Jacobsthal Numbers:");
for (i, n) in jacobsthal_numbers().take(30).enumerate() {
print!("{:9}{}", n, if (i + 1) % 5 == 0 { "\n" } else { " " });
}
println!("\nFirst 30 Jacobsthal-Lucas Numbers:");
for (i, n) in jacobsthal_lucas_numbers().take(30).enumerate() {
print!("{:9}{}", n, if (i + 1) % 5 == 0 { "\n" } else { " " });
}
println!("\nFirst 20 Jacobsthal oblong Numbers:");
for (i, n) in jacobsthal_oblong_numbers().take(20).enumerate() {
print!("{:11}{}", n, if (i + 1) % 5 == 0 { "\n" } else { " " });
}
println!("\nFirst 20 Jacobsthal primes:");
for n in jacobsthal_primes().take(20) {
println!("{}", n);
}
}
```
Output:
```First 30 Jacobsthal Numbers:
0         1         1         3         5
11        21        43        85       171
341       683      1365      2731      5461
10923     21845     43691     87381    174763
349525    699051   1398101   2796203   5592405
11184811  22369621  44739243  89478485 178956971

First 30 Jacobsthal-Lucas Numbers:
2         1         5         7        17
31        65       127       257       511
1025      2047      4097      8191     16385
32767     65537    131071    262145    524287
1048577   2097151   4194305   8388607  16777217
33554431  67108865 134217727 268435457 536870911

First 20 Jacobsthal oblong Numbers:
0           1           3          15          55
231         903        3655       14535       58311
232903      932295     3727815    14913991    59650503
238612935   954429895  3817763271 15270965703 61084037575

First 20 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
2932031007403
768614336404564651
201487636602438195784363
845100400152152934331135470251
56713727820156410577229101238628035243
62357403192785191176690552862561408838653121833643
1046183622564446793972631570534611069350392574077339085483
267823007376498379256993682056860433753700498963798805883563
5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443
```

## SETL

```program jacobsthal_numbers;
print("First 30 Jacobsthal numbers:");
printseq([j n : n in [0..29]]);
print;

print("First 30 Jacobsthal-Lucas numbers:");
printseq([jl n : n in [0..29]]);
print;

print("First 20 Jacobsthal oblong numbers:");
printseq([jo n : n in [0..19]]);
print;

print("First 10 Jacobsthal primes:");
printseq([j n : n in [0..31] | prime j n]);

proc printseq(seq);
loop for n in seq do
if (i +:= 1) mod 5 = 0 then print; end if;
end loop;
end proc;

op j(n);
return (2**n - (-1)**n) div 3;
end op;

op jl(n);
return 2**n + (-1)**n;
end op;

op jo(n);
return j n * j (n+1);
end op;

op prime(n);
if n<=4 then return n in {2,3}; end if;
return not exists d in [2..floor sqrt n] | n mod d = 0;
end op;
end program;```
Output:
```First 30 Jacobsthal numbers:
0             1             1             3             5
11            21            43            85           171
341           683          1365          2731          5461
10923         21845         43691         87381        174763
349525        699051       1398101       2796203       5592405
11184811      22369621      44739243      89478485     178956971

First 30 Jacobsthal-Lucas numbers:
2             1             5             7            17
31            65           127           257           511
1025          2047          4097          8191         16385
32767         65537        131071        262145        524287
1048577       2097151       4194305       8388607      16777217
33554431      67108865     134217727     268435457     536870911

First 20 Jacobsthal oblong numbers:
0             1             3            15            55
231           903          3655         14535         58311
232903        932295       3727815      14913991      59650503
238612935     954429895    3817763271   15270965703   61084037575

First 10 Jacobsthal primes:
3             5            11            43           683
2731         43691        174763       2796203     715827883```

## Sidef

```func jacobsthal(n) {
lucasU(1, -2, n)
}

func lucas_jacobsthal(n) {
lucasV(1, -2, n)
}

say "First 30 Jacobsthal numbers:"
say 30.of(jacobsthal)

say "\nFirst 30 Jacobsthal-Lucas numbers:"
say 30.of(lucas_jacobsthal)

say "\nFirst 20 Jacobsthal oblong numbers:"
say 21.of(jacobsthal).cons(2, {|a,b| a * b })

say "\nFirst 20 Jacobsthal primes:";
say (1..Inf -> lazy.map(jacobsthal).grep{.is_prime}.first(20))
```
Output:
```First 30 Jacobsthal numbers:
[0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763, 349525, 699051, 1398101, 2796203, 5592405, 11184811, 22369621, 44739243, 89478485, 178956971]

First 30 Jacobsthal-Lucas numbers:
[2, 1, 5, 7, 17, 31, 65, 127, 257, 511, 1025, 2047, 4097, 8191, 16385, 32767, 65537, 131071, 262145, 524287, 1048577, 2097151, 4194305, 8388607, 16777217, 33554431, 67108865, 134217727, 268435457, 536870911]

First 20 Jacobsthal oblong numbers:
[0, 1, 3, 15, 55, 231, 903, 3655, 14535, 58311, 232903, 932295, 3727815, 14913991, 59650503, 238612935, 954429895, 3817763271, 15270965703, 61084037575]

First 20 Jacobsthal primes:
[3, 5, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, 2932031007403, 768614336404564651, 201487636602438195784363, 845100400152152934331135470251, 56713727820156410577229101238628035243, 62357403192785191176690552862561408838653121833643, 1046183622564446793972631570534611069350392574077339085483, 267823007376498379256993682056860433753700498963798805883563, 5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731, 95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443]
```

## uBasic/4tH

Translation of: FreeBASIC
```Dim @n(2)
x = 0
y = 1
p = 1
q = -2

Print "First 30 Jacobsthal numbers:"
c = 0 : @n(x) = 0: @n(y) = 1
For j = 0 To 29
c = c + 1
Print Using " ____________#"; @n(x);
If (c % 5) = 0 Then Print
@n(x) = P * @n(y) - Q * @n(x)
Push x : x = y : y = Pop()
Next

Print : Print "First 30 Jacobsthal-Lucas numbers: "
c = 0 : @n(x) = 2: @n(y) = 1
For j = 0 To 29
c = c + 1
Print Using " ____________#"; @n(x);
If (c % 5) = 0 Then Print
@n(x) = P * @n(y) - Q * @n(x)
Push x : x = y : y = Pop()
Next

Print : Print "First 20 Jacobsthal oblong numbers: "
c = 0 : @n(x) = 0: @n(y) = 1
For j = 0 To 19
c = c + 1
Print Using " ____________#"; @n(x)*@n(y);
If (c % 5) = 0 Then Print
@n(x) = P * @n(y) - Q * @n(x)
Push x : x = y : y = Pop()
Next

Print : Print "First 10 Jacobsthal primes: "
c = 0 : @n(x) = 0 : @n(y) = 1
Do
If FUNC(_isPrime(@n(x))) Then c = c + 1 : Print @n(x)
@n(x) = P * @n(y) - Q * @n(x)
Push x : x = y : y = Pop()
Until c = 10
Loop

End

_isPrime
Param (1)
Local (1)

If (a@ < 2) Then Return (0)
If (a@ % 2) = 0 Then Return (0)
For b@ = 3 To Func(_Sqrt(a@, 0))+1 Step 2
If (a@ % b@) = 0 Then Unloop : Return (0)
Next
Return (1)

_Sqrt
Param (2)
Local (2)

If a@ = 0 Return (0)
c@ = Max(Shl(Set(a@, a@*(10^(b@*2))), -10), 1024)

Do
d@ = (c@+a@/c@)/2
While (c@ > d@)
c@ = d@
Loop
Return (c@)```
Output:
```First 30 Jacobsthal numbers:
0             1             1             3             5
11            21            43            85           171
341           683          1365          2731          5461
10923         21845         43691         87381        174763
349525        699051       1398101       2796203       5592405
11184811      22369621      44739243      89478485     178956971

First 30 Jacobsthal-Lucas numbers:
2             1             5             7            17
31            65           127           257           511
1025          2047          4097          8191         16385
32767         65537        131071        262145        524287
1048577       2097151       4194305       8388607      16777217
33554431      67108865     134217727     268435457     536870911

First 20 Jacobsthal oblong numbers:
0             1             3            15            55
231           903          3655         14535         58311
232903        932295       3727815      14913991      59650503
238612935     954429895    3817763271   15270965703   61084037575

First 10 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883

0 OK, 0:1024 ```

## V (Vlang)

Translation of: go
 This example is incomplete. Probably Prime section isn't implemented yet (This is in development) Please ensure that it meets all task requirements and remove this message.
```import math.big

fn jacobsthal(n u32) big.Integer {
mut t := big.one_int
t=t.lshift(n)
mut s := big.one_int
if n%2 != 0 {
s=s.neg()
}
t -= s
return t/big.integer_from_int(3)
}

fn jacobsthal_lucas(n u32) big.Integer {
mut t := big.one_int
t=t.lshift(n)
mut a := big.one_int
if n%2 != 0 {
a=a.neg()
}
return t+a
}

fn main() {
mut jac := []big.Integer{len: 30}
println("First 30 Jacobsthal numbers:")
for i := u32(0); i < 30; i++ {
jac[i] = jacobsthal(i)
print("\${jac[i]:9} ")
if (i+1)%5 == 0 {
println('')
}
}

println("\nFirst 30 Jacobsthal-Lucas numbers:")
for i := u32(0); i < 30; i++ {
print("\${jacobsthal_lucas(i):9} ")
if (i+1)%5 == 0 {
println('')
}
}

println("\nFirst 20 Jacobsthal oblong numbers:")
for i := u32(0); i < 20; i++ {
print("\${jac[i]*jac[i+1]:11} ")
if (i+1)%5 == 0 {
println('')
}
}

/*println("\nFirst 20 Jacobsthal primes:")
for n, count := u32(0), 0; count < 20; n++ {
j := jacobsthal(n)
if j.probably_prime(10) {
println(j)
count++
}
}*/
}```
Output:
```First 30 Jacobsthal numbers:
0            1            1            3            5
11           21           43           85          171
341          683        1,365        2,731        5,461
10,923       21,845       43,691       87,381      174,763
349,525      699,051    1,398,101    2,796,203    5,592,405
11,184,811   22,369,621   44,739,243   89,478,485  178,956,971

First 30 Jacobsthal-Lucas numbers:
2            1            5            7           17
31           65          127          257          511
1,025        2,047        4,097        8,191       16,385
32,767       65,537      131,071      262,145      524,287
1,048,577    2,097,151    4,194,305    8,388,607   16,777,217
33,554,431   67,108,865  134,217,727  268,435,457  536,870,911

First 20 Jacobsthal oblong numbers:
0              1              3             15             55
231            903          3,655         14,535         58,311
232,903        932,295      3,727,815     14,913,991     59,650,503
238,612,935    954,429,895  3,817,763,271 15,270,965,703 61,084,037,575

```

## Wren

Library: Wren-big
Library: Wren-seq
Library: Wren-fmt
```import "./big" for BigInt
import "./seq" for Lst
import "./fmt" for Fmt

var jacobsthal = Fn.new { |n| ((BigInt.one << n) - ((n%2 == 0) ? 1 : -1)) / 3 }

var jacobsthalLucas = Fn.new { |n| (BigInt.one << n) + ((n%2 == 0) ? 1 : -1) }

System.print("First 30 Jacobsthal numbers:")
var js = (0..29).map { |i| jacobsthal.call(i) }.toList
Fmt.tprint("\$,12i", js, 5)

System.print("\nFirst 30 Jacobsthal-Lucas numbers:")
var jsl = (0..29).map { |i| jacobsthalLucas.call(i) }.toList
Fmt.tprint("\$,12i", jsl, 5)

System.print("\nFirst 20 Jacobsthal oblong numbers:")
var oblongs = (0..19).map { |i| js[i] * js[i+1] }.toList
Fmt.tprint("\$,14i", oblongs, 5)

var primes = js.where { |j| j.isProbablePrime(10) }.toList
var count = primes.count
var i = 31
while (count < 20) {
var j = jacobsthal.call(i)
if (j.isProbablePrime(10)) {
count = count + 1
}
i = i + 1
}
System.print("\nFirst 20 Jacobsthal primes:")
for (i in 0..19) Fmt.print("\$i", primes[i])
```
Output:
```First 30 Jacobsthal numbers:
0            1            1            3            5
11           21           43           85          171
341          683        1,365        2,731        5,461
10,923       21,845       43,691       87,381      174,763
349,525      699,051    1,398,101    2,796,203    5,592,405
11,184,811   22,369,621   44,739,243   89,478,485  178,956,971

First 30 Jacobsthal-Lucas numbers:
2            1            5            7           17
31           65          127          257          511
1,025        2,047        4,097        8,191       16,385
32,767       65,537      131,071      262,145      524,287
1,048,577    2,097,151    4,194,305    8,388,607   16,777,217
33,554,431   67,108,865  134,217,727  268,435,457  536,870,911

First 20 Jacobsthal oblong numbers:
0              1              3             15             55
231            903          3,655         14,535         58,311
232,903        932,295      3,727,815     14,913,991     59,650,503
238,612,935    954,429,895  3,817,763,271 15,270,965,703 61,084,037,575

First 20 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
2932031007403
768614336404564651
201487636602438195784363
845100400152152934331135470251
56713727820156410577229101238628035243
62357403192785191176690552862561408838653121833643
1046183622564446793972631570534611069350392574077339085483
267823007376498379256993682056860433753700498963798805883563
5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443
```

## XPL0

```func IsPrime(N);        \Return 'true' if N is prime
int  N, I;
[if N <= 2 then return N = 2;
if (N&1) = 0 then \even >2\ return false;
for I:= 3 to sqrt(N) do
[if rem(N/I) = 0 then return false;
I:= I+1;
];
return true;
];

proc Jaco(J2);          \Display 30 Jacobsthal (or -Lucas) numbers
real J2, J1, J;
int  N;
[RlOut(0, J2);
J1:= 1.0;
RlOut(0, J1);
for N:= 2 to 30-1 do
[J:= J1 + 2.0*J2;
RlOut(0, J);
if rem((N+1)/5) = 0 then CrLf(0);
J2:= J1;  J1:= J;
];
CrLf(0);
];

real J, J1, J2, JO;
int  N;
[Format(14, 0);
Jaco(0.0);
Jaco(2.0);
J2:= 1.0;
RlOut(0, 0.0);
J1:= 1.0;
RlOut(0, J1);
for N:= 2 to 20-1 do
[J:= (J1 + 2.0*J2);
JO:= J*J1;
RlOut(0, JO);
if rem((N+1)/5) = 0 then CrLf(0);
J2:= J1;  J1:= J;
];
CrLf(0);
J2:= 0.0;  J1:= 1.0;  N:= 0;
loop    [J:= J1 + 2.0*J2;
if IsPrime(fix(J)) then
[RlOut(0, J);
N:= N+1;
if rem(N/5) = 0 then CrLf(0);
if N >= 10 then quit;
];
J2:= J1;  J1:= J;
];
]```
Output:
```             0             1             1             3             5
11            21            43            85           171
341           683          1365          2731          5461
10923         21845         43691         87381        174763
349525        699051       1398101       2796203       5592405
11184811      22369621      44739243      89478485     178956971

2             1             5             7            17
31            65           127           257           511
1025          2047          4097          8191         16385
32767         65537        131071        262145        524287
1048577       2097151       4194305       8388607      16777217
33554431      67108865     134217727     268435457     536870911

0             1             3            15            55
231           903          3655         14535         58311
232903        932295       3727815      14913991      59650503
238612935     954429895    3817763271   15270965703   61084037575

3             5            11            43           683
2731         43691        174763       2796203     715827883
```