Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Dec 07 2018 12:25:35
%S 2,5,7,13,23,29,31,43,47,53,59,79,83,97,137,139,173,191,227,239,241,
%T 257,263,281,317,331,337,349,353,359,373,383,421,439,443,449,461,463,
%U 467,479,499,509,523,547,557,563,569,593,599,607,619,641,643,653,659
%N 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.
%C For s(p,k_1)=5 and s(p,k_1)=7 see A251964 and A252280 respectively.
%t 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 *)
%o (PARI) s(p,k) = my(s=sumdigits(p^k)); s >> valuation(s, 2);
%o f11(p) = my(k=1); while(s(p,k) % 11, k++); k;
%o isok11(p) = s(p, f11(p)) == 11;
%o lista11(nn) = forprime(p=2, nn, if (isok11(p), print1(p, ", "))); \\ _Michel Marcus_, Dec 07 2018
%Y Cf. A221858, A225039, A225093, A251964, A252280.
%K nonn,base
%O 1,1
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Dec 16 2014