A252281 For a prime p, denote by s(p,k) the odd part of the digital sum of p^k. Let k_1 be the smallest k such that s(p,k) is divisible by 11. Sequence lists primes p for which s(p,k_1)=11.

2, 5, 7, 13, 23, 29, 31, 43, 47, 53, 59, 79, 83, 97, 137, 139, 173, 191, 227, 239, 241, 257, 263, 281, 317, 331, 337, 349, 353, 359, 373, 383, 421, 439, 443, 449, 461, 463, 467, 479, 499, 509, 523, 547, 557, 563, 569, 593, 599, 607, 619, 641, 643, 653, 659

Offset: 1

Author

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

Keywords

• nonn
• base

Comments

For s(p,k_1)=5 and s(p,k_1)=7 see A251964 and A252280 respectively.

Crossrefs

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

Programs

Mathematica

s[p_, k_] := Module[{s = Total[IntegerDigits[p^k]]}, s/2^IntegerExponent[s, 2]]; f11[p_] := Module[{k = 1}, While[! Divisible[s[p, k], 11], k++]; k]; ok11Q[p_] := s[p, f11[p]] == 11; Select[Range[1000], PrimeQ[#] && ok11Q[#] &] (* Amiram Eldar, Dec 07 2018 *)

PARI

s(p,k) = my(s=sumdigits(p^k)); s >> valuation(s, 2);
f11(p) = my(k=1); while(s(p,k) % 11, k++); k;
isok11(p) = s(p, f11(p)) == 11;
lista11(nn) = forprime(p=2, nn, if (isok11(p), print1(p, ", "))); \\ Michel Marcus, Dec 07 2018