|
%I #11 Dec 08 2018 16:06:42
%S 2,5,7,11,19,37,41,61,71,73,101,109,127,163,181,211,241,271,307,313,
%T 383,421,433,523,541,587,601,613,631,811,947,971,983,1013,1031,1033,
%U 1063,1123,1153,1171,1201,1229,1303,1423,1483,1531,1621,1973,2053,2113,2207,2311,2341
%N Intersection of A251964 and A252280.
%C 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.
%C Sequence lists primes p for which s(p,k_1)=5 and s(p,k_2)=7.
%t 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 *)
%o (PARI) s(p,k) = my(s=sumdigits(p^k)); s >> valuation(s, 2);
%o f5(p) = my(k=1); while(s(p,k) % 5, k++); k;
%o isok5(p) = s(p, f5(p)) == 5;
%o f7(p) = my(k=1); while(s(p,k) % 7, k++); k;
%o isok7(p) = s(p, f7(p)) == 7;
%o lista(nn) = forprime(p=2, nn, if (isok5(p) && isok7(p), print1(p, ", "))); \\ _Michel Marcus_, Dec 08 2018
%Y Cf. A221858, A225039, A225093, A251964, A252280, A252281.
%K nonn,base
%O 1,1
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Dec 16 2014
%E More terms from _Michel Marcus_, Dec 08 2018
|
