A346493 Primes p such that the sum of digits of p and digits of the next prime q is equal to the sum of digits of p*q

251, 503, 971, 1223, 1907, 2579, 2897, 3191, 3761, 3797, 4397, 4919, 5003, 5147, 5261, 5273, 5483, 6047, 6263, 6353, 6911, 7523, 7541, 8069, 8501, 8807, 9413, 9467, 10853, 11471, 11483, 11897, 11933, 12473, 13751, 14741, 15161, 15461, 15629, 15767, 16091, 16301, 16889, 16937, 18077, 18143, 18329, 19163

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 971 is a term because 971 is prime, the next prime is 977, 971*977 = 948667, and 9+7+1+9+7+7 = 40 = 9+4+8+6+6+7.

Maple

q:= 2: sq:= q;
R:= NULL: count:= 0:
while count < 100 do
  p:= q; sp:= sq;
  q:= nextprime(q);
  sq:= convert(convert(q, base, 10), `+`);
  if sp+sq = convert(convert(p*q, base, 10), `+`) then
    R:= R, p; count:= count+1;
  fi
od:
R;

Mathematica

Select[Prime@Range@3000, Total@Flatten[IntegerDigits/@(t=NextPrime[#, {0, 1}])]==Total@IntegerDigits[Times@@t]&] (* Giorgos Kalogeropoulos, Jul 20 2021 *)

Prog

(PARI) isok(p) = if (isprime(p), my(q=nextprime(p+1)); sumdigits(p)+sumdigits(q) == sumdigits(p*q)); \\ Michel Marcus, Jul 20 2021

Crossrefs

Cf. A007605

Sequence in context: A142569 A142742 A142924 * A107696 A001135 A052232

Adjacent sequences: A346490 A346491 A346492 * A346494 A346495 A346496

Keyword

nonn,base

Author

J. M. Bergot and Robert Israel, Jul 19 2021

Status

approved