Strange plus numbers: Difference between revisions
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return 0;
}</lang>
{{out}}
<pre>111 112 114 116 120 121 123 125 129 141
143 147 149 161 165 167 202 203 205 207
211 212 214 216 230 232 234 238 250 252
256 258 292 294 298 302 303 305 307 320
321 323 325 329 341 343 347 349 383 385
389 411 412 414 416 430 432 434 438 470
474 476 492 494 498</pre>
=={{header|COBOL}}==
<lang cobol> IDENTIFICATION DIVISION.
PROGRAM-ID. STRANGE-PLUS-NUMBERS.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 VARIABLES.
03 CANDIDATE PIC 999.
03 DIGITS REDEFINES CANDIDATE,
PIC 9 OCCURS 3 TIMES.
03 LEFT-PAIR PIC 99.
88 LEFT-PAIR-PRIME VALUES 2, 3, 5, 7, 11, 13, 17.
03 RIGHT-PAIR PIC 99.
88 RIGHT-PAIR-PRIME VALUES 2, 3, 5, 7, 11, 13, 17.
01 OUT.
03 ROW PIC X(40) VALUE SPACES.
03 PTR PIC 99 VALUE 1.
PROCEDURE DIVISION.
BEGIN.
PERFORM CHECK-STRANGE-NUMBER
VARYING CANDIDATE FROM 100 BY 1
UNTIL CANDIDATE IS GREATER THAN 500.
DISPLAY ROW.
STOP RUN.
CHECK-STRANGE-NUMBER.
ADD DIGITS(1), DIGITS(2) GIVING LEFT-PAIR.
ADD DIGITS(2), DIGITS(3) GIVING RIGHT-PAIR.
IF LEFT-PAIR-PRIME AND RIGHT-PAIR-PRIME,
PERFORM WRITE-STRANGE-NUMBER.
WRITE-STRANGE-NUMBER.
STRING CANDIDATE DELIMITED BY SIZE INTO ROW
WITH POINTER PTR.
ADD 1 TO PTR.
IF PTR IS GREATER THAN 40,
DISPLAY ROW,
MOVE SPACES TO ROW,
MOVE 1 TO PTR.</lang>
{{out}}
<pre>111 112 114 116 120 121 123 125 129 141
| |||
Revision as of 12:26, 11 May 2022
n is a strange plus number if the sum of the first two digits is prime and the sum of the second two digits is also prime.
Where 100 < n < 500
- Related task
11l
<lang 11l>F is_strange_plus(n)
V xs = String(n).map(c -> Int(c)) R all(zip(xs, xs[1..]).map((a, b) -> a + b C (2, 3, 5, 7, 11, 13, 17)))
V xs = (100..500).filter(n -> is_strange_plus(n)) print("\n\"Strange Plus\" numbers in range [100..500]\n") print(‘(Total: ’String(xs.len)")\n") L(el) xs
print(el, end' ‘ ’)
I L.index % 10 == 9
print()</lang>
- Output:
"Strange Plus" numbers in range [100..500] (Total: 65) 111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
Action!
<lang Action!>BYTE Func IsStrangePlusNumber(INT i)
BYTE ARRAY primes=[0 0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0] BYTE d,prev,first,sum
prev=255
first=1
WHILE i#0
DO
d=i MOD 10
IF prev#255 THEN
sum=d+prev
IF first=1 AND primes(sum)=0 THEN
RETURN (0)
FI
first=0
FI
prev=d
i==/10
OD
IF primes(sum)=0 THEN
RETURN (0)
FI
RETURN (1)
PROC Main()
INT i,count=[0]
FOR i=101 TO 499
DO
IF IsStrangePlusNumber(i) THEN
PrintI(i) Put(32)
count==+1
FI
OD
PrintF("%E%EThere are %I strange plus numbers",count)
RETURN</lang>
- Output:
Screenshot from Atari 8-bit computer
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498 There are 65 strange plus numbers
ALGOL 68
Does not attempt to generalise beyond 3 digit numbers.
<lang algol68>BEGIN # find numbers where the sum of the first 2 digits is prime and also #
# the sum of the second 2 digits is prime #
# considers numbers n where 100 < n < 500 #
PR read "primes.incl.a68" PR
[]BOOLprime = PRIMESIEVE 18; # note: PRIMESIEVE includes 0 in the sieve #
INT s count := 0;
FOR n FROM 101 TO 499 DO
INT v := n;
INT d1 = v MOD 10; v OVERAB 10;
INT d2 = v MOD 10; v OVERAB 10;
INT d3 = v;
IF prime[ d1 + d2 ] AND prime[ d2 + d3 ] THEN
print( ( " ", whole( n, -3 ) ) );
IF ( s count +:= 1 ) MOD 10 = 0 THEN print( ( newline ) ) FI
FI
OD
END</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
APL
<lang APL>(∧⌿ 2 3 5 7 11 13 17 ∊⍨ 2 +⌿ 10 (⊥⍣¯1) X)/X←100+⍳399</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203
205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294
298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385
389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
AppleScript
<lang applescript>------------------- STRANGE PLUS NUMBERS -----------------
-- isStrangePlus :: Int -> Bool on isStrangePlus(n)
set ds to digits(n)
script sumIsSmallPrime
on |λ|(a, b)
{2, 3, 5, 7, 11, 13, 17} contains (a + b)
end |λ|
end script
zipWith(sumIsSmallPrime, ds, rest of ds) does not contain false
end isStrangePlus
TEST -------------------------
on run
set xs to filter(isStrangePlus, enumFromTo(100, 500))
intercalate("\n\n", ¬
{"'Strange Plus' numbers found in range [100..500]", ¬
"Full list:", ¬
("(total " & (length of xs) as string) & ")", ¬
unlines(map(unwords, chunksOf(10, map(str, xs))))})
end run
GENERIC ------------------------
-- 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
-- digits :: Int -> [Int]
on digits(n)
script go
on |λ|(x)
x as integer
end |λ|
end script
map(go, characters of (n as string))
end digits
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m ≤ n then
set lst to {}
repeat with i from m to n
set end of lst to i
end repeat
lst
else
{}
end if
end enumFromTo
-- intercalate :: String -> [String] -> String
on intercalate(delim, xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, delim}
set s to xs as text
set my text item delimiters to dlm
s
end intercalate
-- filter :: (a -> Bool) -> [a] -> [a]
on filter(p, xs)
tell mReturn(p)
set lst to {}
set lng to length of xs
repeat with i from 1 to lng
set v to item i of xs
if |λ|(v, i, xs) then set end of lst to v
end repeat
if {text, string} contains class of xs then
lst as text
else
lst
end if
end tell
end filter
-- 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
-- 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
-- min :: Ord a => a -> a -> a
on min(x, y)
if y < x then
y
else
x
end if
end min
-- 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
-- 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
-- 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
-- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
on zipWith(f, xs, ys)
set lng to min(length of xs, length of ys)
set lst to {}
if 1 > lng then
return {}
else
tell mReturn(f)
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, item i of ys)
end repeat
return lst
end tell
end if
end zipWith</lang>
- Output:
'Strange Plus' numbers found in range [100..500] Full list: (total 65) 111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
AWK
<lang AWK>
- syntax: GAWK -f STRANGE_PLUS_NUMBERS.AWK
BEGIN {
start = 100
stop = 500
for (i=start; i<=stop; i++) {
c1 = substr(i,1,1)
c2 = substr(i,2,1)
c3 = substr(i,3,1)
if (is_prime(c1 + c2) && is_prime(c2 + c3)) {
printf("%d%1s",i,++count%10?"":"\n")
}
}
printf("\nStrange plus numbers %d-%d: %d\n",start,stop,count)
exit(0)
} function is_prime(x, i) {
if (x <= 1) {
return(0)
}
for (i=2; i<=int(sqrt(x)); i++) {
if (x % i == 0) {
return(0)
}
}
return(1)
} </lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498 Strange plus numbers 100-500: 65
C
Generalized solution: a number is strange iff the sum of two consecutive digits is always prime. Numbers < 10 are considered non-strange.
<lang c>#include <stdio.h>
static int p[19] = {0, 0, 1, 1, 0, 1, 0, 1, 0, 0,
0, 1, 0, 1, 0, 0, 0, 1, 0};
int isstrange(long n) {
if (n < 10) return 0;
for (; n >= 10; n /= 10) {
if (!p[n%10 + (n/10)%10]) return 0;
}
return 1;
}
int main(void) {
long n; int k = 0;
for (n = 101; n < 500; n++) {
if (isstrange(n)) {
printf("%d%c", n, ++k%10 ? ' ' : '\n');
}
}
return 0;
}</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
C++
<lang cpp>#include <iostream>
- include <vector>
const std::vector<bool> p{
false, false, true, true, false, true, false, true, false, false, false, true, false, true, false, false, false, true, false
};
bool isStrange(long n) {
if (n < 10) {
return false;
}
for (; n >= 10; n /= 10) {
if (!p[n % 10 + (n / 10) % 10]) {
return false;
}
}
return true;
}
void test(int nMin, int nMax) {
int k = 0;
for (long n = nMin; n <= nMax;n++) {
if (isStrange(n)) {
std::cout << n;
if (++k % 10 != 0) {
std::cout << ' ';
} else {
std::cout << '\n';
}
}
}
}
int main() {
test(101, 499); return 0;
}</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
COBOL
<lang cobol> IDENTIFICATION DIVISION.
PROGRAM-ID. STRANGE-PLUS-NUMBERS.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 VARIABLES.
03 CANDIDATE PIC 999.
03 DIGITS REDEFINES CANDIDATE,
PIC 9 OCCURS 3 TIMES.
03 LEFT-PAIR PIC 99.
88 LEFT-PAIR-PRIME VALUES 2, 3, 5, 7, 11, 13, 17.
03 RIGHT-PAIR PIC 99.
88 RIGHT-PAIR-PRIME VALUES 2, 3, 5, 7, 11, 13, 17.
01 OUT.
03 ROW PIC X(40) VALUE SPACES.
03 PTR PIC 99 VALUE 1.
PROCEDURE DIVISION.
BEGIN.
PERFORM CHECK-STRANGE-NUMBER
VARYING CANDIDATE FROM 100 BY 1
UNTIL CANDIDATE IS GREATER THAN 500.
DISPLAY ROW.
STOP RUN.
CHECK-STRANGE-NUMBER.
ADD DIGITS(1), DIGITS(2) GIVING LEFT-PAIR.
ADD DIGITS(2), DIGITS(3) GIVING RIGHT-PAIR.
IF LEFT-PAIR-PRIME AND RIGHT-PAIR-PRIME,
PERFORM WRITE-STRANGE-NUMBER.
WRITE-STRANGE-NUMBER.
STRING CANDIDATE DELIMITED BY SIZE INTO ROW
WITH POINTER PTR.
ADD 1 TO PTR.
IF PTR IS GREATER THAN 40,
DISPLAY ROW,
MOVE SPACES TO ROW,
MOVE 1 TO PTR.</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
Delphi
<lang Delphi> program Strange_plus_numbers;
{$APPTYPE CONSOLE}
uses
System.SysUtils;
function IsPrime(n: Integer): Boolean; begin
Result := n in [2, 3, 5, 7, 11, 13, 17];
end;
begin
var count := 0;
var d: TArray<Integer>;
writeln('Strange plus numbers in the open interval (100, 500) are:');
for var i := 101 to 499 do
begin
d := [];
var j := i;
while j > 0 do
begin
SetLength(d, Length(d) + 1);
d[High(d)] := j mod 10;
j := j div 10;
end;
if IsPrime(d[0] + d[1]) and IsPrime(d[1] + d[2]) then
begin
write(i, ' ');
inc(count);
if count mod 10 = 0 then
writeln;
end;
end;
if (count mod 10) <> 0 then writeln;
writeln(#10, count, ' strange plus numbers in all.'); readln;
end.</lang>
F#
This task uses Extensible Prime Generator (F#).
<lang fsharp>
// Strange numbers. Nigel Galloway: February 25th., 2021
let pD=[0..99]|>List.map(fun n->(n/10,n%10))|>List.filter(fun(n,g)->isPrime(n+g))
pD|>List.filter(fun(n,_)->n>0)|>List.map(fun(n,g)->(n,pD|>List.filter(fun(n,_)->n=g)))
|>List.collect(fun(n,g)->g|>List.map(fun(g,k)->n*100+g*10+k))|>List.filter((>)500)|>List.iter(printf "%d ");printfn ""
</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
Factor
<lang factor>USING: grouping grouping.extras io kernel math math.primes math.ranges math.text.utils prettyprint sequences ;
- strange+? ( n -- ? )
dup 10 < [ drop f ] [ 1 digit-groups [ + ] 2 clump-map [ prime? ] all? ] if ;
"Strange plus numbers in (100, 500):" print nl 100 500 (a,b) [ strange+? ] filter dup 10 group [ [ pprint bl ] each nl ] each nl length pprint " strange plus numbers found." print</lang>
- Output:
Strange plus numbers in (100, 500): 111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498 65 strange plus numbers found.
Forth
<lang forth>create isprime false , false , true , true , false ,
true , false , true , false , false , false , true , false , true , false , false , false , true , false ,
\ tests whether n is prime for 0 <= n < 19
- prime? ( n -- ? )
cells isprime + @ ;
- strange? ( n -- ? )
dup 10 < if drop false exit then begin dup 10 >= while dup 10 /mod 10 mod + prime? invert if drop false exit then 10 / repeat drop true ;
- main
0
500 101 do
i strange? if
i .
1+
dup 10 mod 0= if cr then else
then
loop
cr
drop ;
main bye</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
FreeBASIC
<lang freebasic> Function isPrime(valor As Integer) As Boolean
If valor <= 1 Then Return False
For i As Integer = 2 To Int(Sqr(valor))
If valor Mod i = 0 Then Return False
Next i
Return True
End Function
Dim As Integer k = 0 Print !"Los n£meros m s extra¤os son:\n" For m As Integer = 100 To 500
Dim As Integer num1, num2, num3
num1 = Val(Mid(Str(m), 1, 1))
num2 = Val(Mid(Str(m), 2, 1))
num3 = Val(Mid(Str(m), 3, 1))
If isPrime(num1 + num2) And isPrime(num2 + num3) Then
Print Using "####"; m;
k += 1
If k Mod 10 = 0 Then Print
End If
Next m Print !"\n\n"; k; " n£meros m s extra¤os encontrados." Sleep </lang>
- Output:
Los números más extraños son: 111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498 65 números más extraños encontrados.
Fōrmulæ
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.
In this page you can see the program(s) related to this task and their results.
Go
<lang go>package main
import "fmt"
func isPrime(n int) bool {
return n == 2 || n == 3 || n == 5 || n == 7 || n == 11 || n == 13 || n == 17
}
func main() {
count := 0
var d []int
fmt.Println("Strange plus numbers in the open interval (100, 500) are:\n")
for i := 101; i < 500; i++ {
d = d[:0]
j := i
for j > 0 {
d = append(d, j%10)
j /= 10
}
if isPrime(d[0]+d[1]) && isPrime(d[1]+d[2]) {
fmt.Printf("%d ", i)
count++
if count%10 == 0 {
fmt.Println()
}
}
}
if count%10 != 0 {
fmt.Println()
}
fmt.Printf("\n%d strange plus numbers in all.\n", count)
}</lang>
- Output:
Strange plus numbers in the open interval (100, 500) are: 111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498 65 strange plus numbers in all.
Haskell
<lang haskell>import Data.List (intercalate) import Data.List.Split (chunksOf)
STRANGE PLUS NUMBERS -----------------
isStrangePlus :: Int -> Bool isStrangePlus n =
all (\(a, b) -> (a + b) `elem` [2, 3, 5, 7, 11, 13, 17]) $ (zip <*> tail) (digits n)
digits :: Int -> [Int]
digits = fmap (read . return) . show
TEST -------------------------
main =
let xs = filter isStrangePlus [100 .. 500]
in (putStrLn . intercalate "\n\n")
[ "\"Strange Plus\" numbers found in range [100..500]",
"(total " <> (show . length) xs <> ")",
"Full list:",
unlines
(unwords <$> chunksOf 10 (show <$> xs))
]</lang>
- Output:
"Strange Plus" numbers found in range [100..500] (total 65) Full list: 111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
Java
<lang java>public class Strange {
private static final boolean[] p = {
false, false, true, true, false,
true, false, true, false, false,
false, true, false, true, false,
false, false, true, false
};
public static boolean isstrange(long n) {
if (n < 10) return false;
for (; n >= 10; n /= 10) {
if (!p[(int)(n%10 + (n/10)%10)]) return false;
}
return true;
}
public static void main(String[] args) {
long nMin = Long.parseLong(args[0]);
long nMax = Long.parseLong(args[1]);
int k = 0;
for (long n = nMin; n <= nMax; n++) {
if (isstrange(n)) {
System.out.print(n + (++k%10 != 0 ? " " : "\n"));
}
}
}
}</lang>
<lang>java Strange 101 499</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
jq
Works with gojq, the Go implementation of jq
See e.g. Erdős-primes#jq for a suitable implementation of `is_prime`. <lang jq>def nwise($n):
def n: if length <= $n then . else .[0:$n] , (.[$n:] | n) end; n;
def is_strange:
def sum($i): (.[$i:$i+1]|tonumber) + (.[$i+1:$i+2]|tonumber); tostring | length > 2 and (sum(0) | is_prime) and (sum(1) | is_prime) ;
def task:
[range(101; 500)
| select(is_strange)]
| nwise(10)
| join(" ");
task</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
Julia
<lang julia>let
smallprimes = [2, 3, 5, 7, 11, 13, 17] # 0 <= all of these primes <= 18
paired_digit_sums(n) = (d = digits(n); [sum(p) for p in zip(d[1:end-1], d[2:end])])
isstrangeplus(n) = all(x -> x ∈ smallprimes, paired_digit_sums(n))
printed = 0
for n in 100:500
isstrangeplus(n) && print(n, (printed += 1) % 13 == 0 ? "\n" : " ")
end
end
</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
Kotlin
<lang scala>val p = arrayOf(
false, false, true, true, false, true, false, true, false, false, false, true, false, true, false, false, false, true, false
)
fun isStrange(n: Long): Boolean {
if (n < 10) {
return false
}
var nn = n
while (nn >= 10) {
if (!p[(nn % 10 + (nn / 10) % 10).toInt()]) {
return false
}
nn /= 10
}
return true
}
fun test(nMin: Long, nMax: Long) {
var k = 0
for (n in nMin..nMax) {
if (isStrange(n)) {
print(n)
if (++k % 10 != 0) {
print(' ')
} else {
println()
}
}
}
}
fun main() {
test(101, 499)
}</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
Maple
<lang maple>select(n->(u->isprime(add(u[1..2])) and isprime(add(u[2..3])))(convert(n,base,10)),[$101..499]);</lang>
- Output:
[111, 112, 114, 116, 120, 121, 123, 125, 129, 141, 143, 147, 149, 161, 165, 167, 202, 203, 205, 207, 211, 212, 214, 216, 230, 232, 234, 238, 250, 252, 256, 258, 292, 294, 298, 302, 303, 305, 307, 320, 321, 323, 325, 329, 341, 343, 347, 349, 383, 385, 389, 411, 412, 414, 416, 430, 432, 434, 438, 470, 474, 476, 492, 494, 498]
Mathematica/Wolfram Language
<lang Mathematica>Select[Range[101, 499], PrimeQ[Total[IntegerDigits[#];; 2]] && PrimeQ[Total[IntegerDigits[#]2 ;;]] &] Length[%]</lang>
- Output:
{111, 112, 114, 116, 120, 121, 123, 125, 129, 141, 143, 147, 149, 161, 165, 167, 202, 203, 205, 207, 211, 212, 214, 216, 230, 232, 234, 238, 250, 252, 256, 258, 292, 294, 298, 302, 303, 305, 307, 320, 321, 323, 325, 329, 341, 343, 347, 349, 383, 385, 389, 411, 412, 414, 416, 430, 432, 434, 438, 470, 474, 476, 492, 494, 498}
65
Nim
<lang Nim>const Primes = {2, 3, 5, 7, 11, 13, 17}
proc digits(n: 100..999): array[3, int] =
[n div 100, n div 10 mod 10, n mod 10]
var count = 0 for n in 101..<500:
let d = n.digits if d[0] + d[1] in Primes and d[1] + d[2] in Primes: inc count stdout.write n, if count mod 13 == 0: '\n' else: ' '</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
Perl
<lang perl>use strict; use warnings; use feature 'say'; use ntheory 'is_prime';
my($low, $high) = (100, 500); my $n = my @SP = grep { my @d = split ; is_prime $d[0]+$d[1] and is_prime $d[1]+$d[2] } $low+1 .. $high-1; say "Between $low and $high there are $n strange-plus numbers:\n" .
(sprintf "@{['%4d' x $n]}", @SP[0..$n-1]) =~ s/(.{80})/$1\n/gr;</lang>
- Output:
Between 100 and 500 there are 65 strange-plus numbers: 111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
Phix
Using the same approach as Strange_numbers#Phix, so this should similarly scale/count easily to the 28-digit range.
constant poss = apply(true,sq_sub,{{get_primes(-7)},tagset(9,0)}), nxts = apply(true,filter,{poss,{"in"},{{0,9}},{"[]"}}) function strange_plus(integer left, sequence digits, res={}, part="") for i=1 to length(digits) do integer di = digits[i] string pn = part&di+'0' if left=1 then res = append(res,pn) else res = strange_plus(left-1,nxts[di+1],res,pn) end if end for return res end function sequence res = strange_plus(3,tagset(4)) -- (3 digit numbers beginning 1..4) printf(1,"%d strange_plus numbers found: %s\n",{length(res),join(shorten(res,"",5),",")})
- Output:
65 strange_plus numbers found: 111,112,114,116,120,...,474,476,492,494,498
Python
Using sympy.isprime
<lang python>Python 3.8.5 (default, Sep 3 2020, 21:29:08) [MSC v.1916 64 bit (AMD64)] on win32 Type "help", "copyright", "credits" or "license()" for more information. >>> from sympy import isprime
>>> [x for x in range(101,500)
if isprime(sum(int(c) for c in str(x)[:2])) and isprime(sum(int(c) for c in str(x)[1:]))]
[111, 112, 114, 116, 120, 121, 123, 125, 129, 141, 143, 147, 149, 161, 165, 167, 202, 203, 205, 207, 211, 212, 214, 216, 230, 232, 234, 238, 250, 252, 256, 258, 292, 294, 298, 302, 303, 305, 307, 320, 321, 323, 325, 329, 341, 343, 347, 349, 383, 385, 389, 411, 412, 414, 416, 430, 432, 434, 438, 470, 474, 476, 492, 494, 498] >>> </lang>
Or, as we may not need to wake up sympy just to check membership of {2, 3, 5, 7, 11, 13, 17}:
<lang python>Strange Plus Numbers
- isStrangePlus :: Int -> Bool
def isStrangePlus(n):
True all consecutive decimal digit
pairs in n have prime sums.
def test(a, b):
return a + b in [2, 3, 5, 7, 11, 13, 17]
xs = digits(n) return all(map(test, xs, xs[1:]))
- ------------------- TEST AND DISPLAY -------------------
- main :: IO ()
def main():
List and count of Strange Plus Numbers
xs = [
n for n in range(100, 1 + 500)
if isStrangePlus(n)
]
print('\n"Strange Plus" numbers in range [100..500]\n')
print('(Total: ' + str(len(xs)) + ')\n')
print(
'\n'.join(
' '.join(
str(x) for x in row
) for row in chunksOf(10)(xs)
)
)
- ----------------------- GENERIC ------------------------
- 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
divible, 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
- digits :: Int -> [Int]
def digits(n):
Component digits of a decimal number. return [int(c) for c in str(n)]
- MAIN ---
if __name__ == '__main__':
main()</lang>
- Output:
"Strange Plus" numbers in range [100..500] (Total: 65) 111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
Raku
<lang perl6>unit sub MAIN ($start = 100, $end = 500); put +$_, " matching numbers from $start to $end:\n", $_ given
($start .. $end).hyper(:256batch,:8degree).grep: { all .comb.rotor(2 => -1).map: { .sum.is-prime } };</lang>
- Output:
65 matching numbers from 100 to 500: 111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
REXX
<lang rexx>/*REXX pgm lists strange+ integers (within a range); sum of adjacent dec. digs is prime.*/ parse arg LO HI . /*obtain optional arguments from the CL*/ if LO== | LO=="," then LO= 101 /*Not specified? Then use the default.*/ if HI== | HI=="," then HI= 499 /* " " " " " " */ !.= 0; !.2= 1; !.3= 1; !.5= 1; !.7= 1 /*build array of sums that are prime. */
!.11= 1; !.13= 1; !.17= 1 /* " " " " " " " */
$= /*the list of strange+ numbers (so far)*/
- = 0 /* " number " " " " " */
do j=LO to HI; L= length(j) /*look for strange+ numbers in range. */
if L==1 then iterate /*Number too short? Then skip it. */
do k=1 for L-1 /*examine the difference in the digits.*/
parse var j =(k) y +1 z +1 /*get two adjacent decimal digits: Y Z */
sum= y + z /*sum of two adjacent decimal digits. */
if \!.sum then iterate j /*Sum not prime? Then skip this number*/
end /*k*/
#= # + 1 /*bump the number of "strange+" numbers*/
$= $ j /*append the number to the $ list. */
end /*j*/
/*stick a fork in it, we're all done. */
say # ' strange plus numbers found between ' LO " and " HI ' (inclusive)' say say strip($)</lang>
- output when using the default inputs:
65 strange plus numbers found between 101 and 499 (inclusive) 111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
Ring
<lang ring> load "stdlib.ring"
row = 0 see "Strange plus numbers are:" + nl
for n = 100 to 500
flag = 1
str = string(n)
for m = 1 to len(str)-1
num1 = number(str[m])
num2 = number(str[m+1])
pr = num1+num2
if not isprime(pr)
flag = 0
exit
ok
next
if flag = 1
see str + " "
row = row + 1
if row % 10 = 0
see nl
ok
ok
next </lang>
- Output:
Strange plus numbers are: 111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
Ruby
<lang ruby>$p = [
false, false, true, true, false, true, false, true, false, false, false, true, false, true, false, false, false, true, false
]
def isStrange(n)
if n < 10 then
return false
end
while n >= 10 do
if not $p[n % 10 + (n / 10).floor % 10] then
return false
end
n = (n / 10).floor
end
return true
end
def test(nMin, nMax)
k = 0
for n in nMin .. nMax
if isStrange(n) then
print n
k = k + 1
if k % 10 != 0 then
print ' '
else
print "\n"
end
end
end
end
test(101, 499)</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
Seed7
<lang seed7>$ include "seed7_05.s7i";
const func boolean: prime (in integer: number) is
return number in {2, 3, 5, 7, 11, 13, 17};
const func boolean: strange (in var integer: number) is func
result
var boolean: strange is TRUE;
begin
while number > 9 and strange do
if not prime(number rem 10 + number div 10 rem 10) then
strange := FALSE;
end if;
number := number div 10;
end while;
end func;
const proc: main is func
local
var integer: n is 0;
var integer: count is 0;
begin
for n range 101 to 499 do
if strange(n) then
write(n <& " ");
incr(count);
if count rem 13 = 0 then
writeln;
end if;
end if;
end for;
end func;</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
Sidef
<lang ruby>100..500 -> map { .digits }.grep {|d|
is_prime(d[-1]+d[-2]) && is_prime(d[-2]+d[-3])
}.map{ .digits2num }.slices(10).each { .join(' ').say }</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
Vlang
<lang vlang>fn is_prime(n int) bool {
return n == 2 || n == 3 || n == 5 || n == 7 || n == 11 || n == 13 || n == 17
}
fn main() {
mut count := 0
mut d := []int{}
println("Strange plus numbers in the open interval (100, 500) are:\n")
for i := 101; i < 500; i++ {
d = d[..0]
mut j := i
for j > 0 {
d << j%10
j /= 10
}
if is_prime(d[0]+d[1]) && is_prime(d[1]+d[2]) {
print("$i ")
count++
if count%10 == 0 {
println()
}
}
}
if count%10 != 0 {
println()
}
println("\n$count strange plus numbers in all.")
}</lang>
- Output:
Strange plus numbers in the open interval (100, 500) are: 111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498 65 strange plus numbers in all.
Wren
Simple brute force is adequate for this. <lang ecmascript>var primes = [2, 3, 5, 7, 11, 13, 17] var count = 0 var d = [] System.print("Strange plus numbers in the open interval (100, 500) are:\n") for (i in 101..499) {
d.clear()
var j = i
while (j > 0) {
d.add(j % 10)
j = (j/10).floor
}
if (primes.contains(d[0] + d[1]) && primes.contains(d[1] + d[2])) {
System.write("%(i) ")
count = count + 1
if (count % 10 == 0) System.print()
}
} if (count % 10 != 0) System.print() System.print("\n%(count) strange plus numbers in all.")</lang>
- Output:
Strange plus numbers in the open interval (100, 500) are: 111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498 65 strange plus numbers in all.
x86 Assembly
A 16-bit solution for NASM under DOS. Assemble with nasm -fbin strange.asm -o strange.com. The prime sieve up to 18 is hard-coded.
<lang> org 100h
mov cx, 10 ; cl is used for division, ch to count numbers printed on a line
mov si, 101 ; loop index from 101 to 499
mov di, p ; pointer to prime sieve
; p+k is a pointer to the reversed string repr. of the current index
L1 mov ax, si
xor bx, bx ; bx counts characters in the string
L2 div cl ; div by 10 to get last digit
add ah, 48 ; convert digit to ascii
mov [bx+di+k], ah ; store char
test bl, bl ; if it's the first, don't check for prime sum
jz L3
add ah, [bx+di+k-1] ; sum of digits
sub ah, 96 ; adjust for ascii
xchg ah, bl
cmp byte [bx+di], 1 ; is it prime?
jne L6 ; otherwise continue with next number
mov bl, ah ; restore bl
L3 xor ah, ah ; must be zero for the next division
inc bx ; one more char
test al, al ; are there more digits?
jnz L2
L4 mov ah, 2 ; the number is strange, print it char by char
mov dl, [bx+di+k-1]
int 21h
dec bx
jnz L4
mov ah, 2 ; print a space or a newline
mov dl, 32
inc ch
cmp ch, 10 ; if less than 10 on the current line it's a space
jne L5
mov dl, 10 ; otherwise it's a newline
xor ch, ch ; reset the counter when we reach 10
L5 int 21h
L6 inc si ; next number
cmp si, 500 ; and loop until we reach 500
jb L1
int 20h ; return to DOS
p db 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0 k equ $-p</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498
XPL0
<lang XPL0>func StrangePlus(N); int N, A, B, S; [N:= N/10; A:= rem(0); loop [N:= N/10;
B:= rem(0);
S:= A+B;
if S#2 & S#3 & S#5 & S#7 & S#11 & S#13 & S#17 then return false;
if N = 0 then return true;
A:= B];
];
int Cnt, N; [Cnt:= 0; for N:= 100 to 500-1 do
if StrangePlus(N) then
[Cnt:= Cnt+1;
IntOut(0, N);
if rem(Cnt/20) = 0 then CrLf(0) else ChOut(0, ^ )];
]</lang>
- Output:
111 112 114 116 120 121 123 125 129 141 143 147 149 161 165 167 202 203 205 207 211 212 214 216 230 232 234 238 250 252 256 258 292 294 298 302 303 305 307 320 321 323 325 329 341 343 347 349 383 385 389 411 412 414 416 430 432 434 438 470 474 476 492 494 498