A252282 Intersection of A251964 and A252280.

2, 5, 7, 11, 19, 37, 41, 61, 71, 73, 101, 109, 127, 163, 181, 211, 241, 271, 307, 313, 383, 421, 433, 523, 541, 587, 601, 613, 631, 811, 947, 971, 983, 1013, 1031, 1033, 1063, 1123, 1153, 1171, 1201, 1229, 1303, 1423, 1483, 1531, 1621, 1973, 2053, 2113, 2207, 2311, 2341

Offset: 1

Author

Vladimir Shevelev and Peter J. C. Moses, Dec 16 2014

Keywords

• nonn
• base

Comments

For a prime p, denote by s(p,k) the odd part of the digital sum of p^k. Let, for the first time, s(p,k) be divisible of 5 for k=k_1 and be divisible of 7 for k=k_2.

Sequence lists primes p for which s(p,k_1)=5 and s(p,k_2)=7.

Crossrefs

Cf. A221858, A225039, A225093, A251964, A252280, A252281.

Programs

Mathematica

s[p_, k_] := Module[{s = Total[IntegerDigits[p^k]]}, s/2^IntegerExponent[s, 2]]; f[p_, q_] := Module[{k = 1}, While[! Divisible[s[p, k], q], k++]; k]; okQ[p_, q_] := s[p, f[p, q]] == q; Select[Range[2400],  PrimeQ[#] && okQ[#, 5] && okQ[#, 7] &] (* Amiram Eldar, Dec 08 2018 *)

PARI

s(p,k) = my(s=sumdigits(p^k)); s >> valuation(s, 2);
f5(p) = my(k=1); while(s(p,k) % 5, k++); k;
isok5(p) = s(p, f5(p)) == 5;
f7(p) = my(k=1); while(s(p,k) % 7, k++); k;
isok7(p) = s(p, f7(p)) == 7;
lista(nn) = forprime(p=2, nn, if (isok5(p) && isok7(p), print1(p, ", "))); \\ Michel Marcus, Dec 08 2018

Extensions

More terms from Michel Marcus, Dec 08 2018