Sum of square and cube digits of an integer are primes

Sum of square and cube digits of an integer are primes is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Task

Find and show here all positive integers n less than 100 where:

• the sum of the digits of the square of n is prime; and
• the sum of the digits of the cube of n is also prime.

Example

16 satisfies the task descrption because 16 x 16 = 256 has a digit sum of 13 which is prime and 16 x 16 x 16 = 4096 has a digit sum of 19 which is also prime.

ALGOL 68

Library: ALGOL 68-primes

<lang algol68>BEGIN # find numbers where the digit sums of the square and cube are prtime #

   INT max number = 99; # maximum number to consider #
   PR read "primes.incl.a68" PR
   []BOOL prime = PRIMESIEVE ( max number * max number * max number );
   # returns the sum of the digits of n #
   OP  DIGITSUM = ( INT n )INT:
       BEGIN
           INT v      := ABS n;
           INT result := v MOD 10;
           WHILE ( v OVERAB 10 ) > 0 DO
               result +:= v MOD 10
           OD;
           result
       END # DIGITSUM # ;
   FOR i TO max number DO
       INT i2 = i * i;
       IF prime[ DIGITSUM i2 ] THEN
           IF prime[ DIGITSUM ( i * i2 ) ] THEN
               print( ( " ", whole( i, 0 ) ) )
           FI
       FI
   OD

END</lang>

Output:

 16 17 25 28 34 37 47 52 64

F#

This task uses Extensible Prime Generator (F#) <lang fsharp> // Sum of square and cube digits of an integer are primes. Nigel Galloway: December 22nd., 2021 let rec fN g=function 0->g |n->fN(g+n%10)(n/10) [1..99]|>List.filter(fun g->isPrime(fN 0 (g*g)) && isPrime(fN 0 (g*g*g)))|>List.iter(printf "%d "); printfn "" </lang>

Output:

16 17 25 28 34 37 47 52 64

Phix

with javascript_semantics
function ipsd(integer n) return is_prime(sum(sq_sub(sprintf("%d",n),'0'))) end function
function scdp(integer n) return ipsd(n*n) and ipsd(n*n*n) end function
pp(filter(tagset(99),scdp))

Output:

{16,17,25,28,34,37,47,52,64}

Raku

<lang perl6>say ^100 .grep: { .².comb.sum.is-prime && .³.comb.sum.is-prime }</lang>

Output:

(16 17 25 28 34 37 47 52 64)

Ring

<lang ring> load "stdlib.ring" see "working..." +nl

limit = 100

for n = 1 to limit

   sums = 0
   sumc = 0
   sps = string(pow(n,2))
   spc = string(pow(n,3))
   for m = 1 to len(sps)
       sums = sums + sps[m]
   next
   for p = 1 to len(spc)
       sumc = sumc + spc[p]
   next
   if isprime(sums) and isprime(sumc)
      see "" + n + " "
   ok

next

see nl + "done..." + nl </lang>

Output:

working...
16 17 25 28 34 37 47 52 64 
done...

Wren

Library: Wren-math

<lang ecmascript>import "./math" for Int

for (i in 1..99) {

   if (Int.isPrime(Int.digitSum(i*i)) && Int.isPrime(Int.digitSum(i*i*i))) System.write("%(i) ")

} System.print()</lang>

Output:

16 17 25 28 34 37 47 52 64 

XPL0

<lang XPL0>func IsPrime(N); \Return 'true' if N is prime int N, I; [if N <= 2 then return N = 2; if (N&1) = 0 then \even >2\ return false; for I:= 3 to sqrt(N) do

   [if rem(N/I) = 0 then return false;
   I:= I+1;
   ];

return true; ];

func SumDigits(N); \Return the sum of digits in N int N, Sum; [Sum:= 0; while N do

   [N:= N/10;
   Sum:= Sum + rem(0);
   ];

return Sum; ];

int N; [for N:= 0 to 100-1 do

   if IsPrime(SumDigits(N*N)) & IsPrime(SumDigits(N*N*N)) then
       [IntOut(0, N);  ChOut(0, ^ )];

]</lang>

Output:

16 17 25 28 34 37 47 52 64