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

1,1

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.

Links

Table of n, a(n) for n=1..53.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A184774 A038884 A338345 * A337497 A040122 A318207

Adjacent sequences: A252279 A252280 A252281 * A252283 A252284 A252285

Keyword

nonn,base

Author

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

Extensions

More terms from Michel Marcus, Dec 08 2018

Status

approved