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# 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

## 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    ODEND`
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 outputend 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 trueend 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) & txtend 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 outputend chopList on matrixToText(matrix, w)    script o        property matrix : missing value        property row : missing value    end script     set o's matrix to matrix    set padding to "                   "    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 txtend join on task()    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)end task task() `
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))) & linefeedend fShow  -- justifyRight :: Int -> Char -> String -> Stringon 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 scriptend 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 -> Stringon 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 xsend replicate  -- table :: Int -> [String] -> Stringon 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] -> Stringon 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    send unlines  -- until :: (a -> Bool) -> (a -> a) -> a -> aon |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    vend |until|  -- unwords :: [String] -> Stringon 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 send unwords  ------------------------- GENERIC ------------------------ -- Just :: a -> Maybe aon 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 aon 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 -> Numon abs(x)    -- Absolute value.    if 0 > x then        -x    else        x    end ifend abs  -- any :: (a -> Bool) -> [a] -> Boolon 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 tellend 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 -> Stringon drop(n, xs)    take(n, xs) -- consumed    xsend 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 xsend 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 scriptend filter  -- isPrime :: Int -> Boolon 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] -> Inton |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 ifend |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 tellend map  -- max :: Ord a => a -> a -> aon max(x, y)    if x > y then        x    else        y    end ifend 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 ifend mReturn  -- mul (*) :: Num a => a -> a -> aon mul(a, b)    a * bend mul  -- signum :: Num -> Numon signum(x)    if x < 0 then        -1    else if x = 0 then        0    else        1    end ifend 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 ifend splitAt  -- str :: a -> Stringon str(x)    x as stringend str  -- take :: Int -> [a] -> [a]-- take :: Int -> String -> Stringon 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 ysend 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 ifend 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 scriptend 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 scriptend 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)/3JL: function [n]-> (2^n) + (neg 1)^nJO: 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] 30printFirst "Jacobsthal-Lucas numbers" 'JL [true] 30printFirst "Jacobsthal oblong numbers" 'JO [true] 20printFirst "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```

## 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);    mpz_add(r, r, 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++

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
```

## Factor

Works with: Factor version 0.99 2021-06-02
`USING: grouping io kernel lists lists.lazy math math.functionsmath.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:" print30 jacobsthals show "First 30 Jacobsthal-Lucas numbers:" print30 lucas-jacobthals show "First 20 Jacobsthal oblong numbers:" print20 oblong show "First 20 Jacobsthal primes:" print20 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 trueEnd Function Dim Shared As Uinteger n(1) Dim Shared As Uinteger i0 = 0, i1 = 1Dim Shared As Integer j, c, P = 1, Q = -2 Print "First 30 Jacobsthal numbers:"c = 0 : n(i0) = 0: n(i1) = 1For 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) = 1For 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) = 1For 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, i1Next j Print !"\n\nFirst 10 Jacobsthal primes: "c = 0 : n(i0) = 0: n(i1) = 1Do    If isPrime(n(i0)) Then c += 1 : Print n(i0)    n(i0) = P * n(i1) - Q * n(i0)    Swap i0, i1Loop Until c = 10Sleep`
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```

## 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)    }    return t.Add(t, 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 -> BoolisPrime 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]) -> Stringformat (k, n, xs) =  show n <> (' ' : k) <> ":\n"    <> table      "  "      (chunksOf 5 \$ show <\$> take n xs) table :: String -> [[String]] -> Stringtable 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. Jacobsthaljl=:      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    174763349525 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    5242871048577 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       58311232903 932295 3727815 14913991 59650503 238612935 954429895 3817763271 15270965703 61084037575   ja I.1 p:ja i.32  NB. first ten Jacobsthal primes3 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 arraysdef 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 tasks:  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)); tasks`
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 Lazyusing Primes J(n) = (2^n - (-1)^n) ÷ 3L(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
```

## 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

printf(1,"First 30 Jacobsthal numbers:\n%s\n",       {join_by(apply(true,sprintf,{{"%9d" },apply(tagset(29,0),jacobsthal)}),1,5," ")})
printf(1,"First 30 Jacobsthal-Lucas numbers:\n%s\n", {join_by(apply(true,sprintf,{{"%9d" },apply(tagset(29,0),jacobsthal_lucas)}),1,5," ")})
printf(1,"First 20 Jacobsthal oblong numbers:\n%s\n",{join_by(apply(true,sprintf,{{"%11d"},apply(tagset(19,0),jacobsthal_oblong)}),1,5," ")})
--printf(1,"First 10 Jacobsthal primes:\n%s\n",    {join(apply(true,sprintf,{{"%d"},filter(apply(tagset(31,0),jacobsthal),is_prime)}),"\n")})
--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/pythonfrom 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 islicefrom operator import mul  # jacobsthal :: [Integer]def jacobsthal():    '''Infinite sequence of terms of OEIS A001045    '''    return jacobsthalish(0, 1)  # jacobsthalish :: (Int, Int) -> [Int]def jacobsthalish(x, y):    '''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)((x, y))  # ------------------------- 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]) -> Stringdef 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 -> Stringdef 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 -> Booldef 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 -> Stringdef 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]] -> Stringdef 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```

## 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: 0while [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
```

## 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
```

## 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]
```

## Wren

Library: Wren-big
Library: Wren-seq
Library: Wren-fmt
`import "./big" for BigIntimport "./seq" for Lstimport "./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) }.toListfor (chunk in Lst.chunks(js, 5)) Fmt.print("\$,12i", chunk) System.print("\nFirst 30 Jacobsthal-Lucas numbers:")var jsl = (0..29).map { |i| jacobsthalLucas.call(i) }.toListfor (chunk in Lst.chunks(jsl, 5)) Fmt.print("\$,12i", chunk) System.print("\nFirst 20 Jacobsthal oblong numbers:")var oblongs = (0..19).map { |i| js[i] * js[i+1] }.toListfor (chunk in Lst.chunks(oblongs, 5)) Fmt.print("\$,14i", chunk) var primes = js.where { |j| j.isProbablePrime(10) }.toListvar count = primes.countvar i = 31while (count < 20) {    var j = jacobsthal.call(i)    if (j.isProbablePrime(10)) {        primes.add(j)        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 primeint  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) numbersreal 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
```