cp's OEIS Frontend

A252666 Let k be the smallest number such that s(k) = odd part of digital sum of 2^k is multiple of prime(n); then a(n)=k, if s(k) = prime(n). Otherwise, or if there is no such k, a(n)=0.

%I A252666 #19 Oct 15 2019 08:38:19
%S A252666 5,4,7,8,47,12,42,19,20,24,23,28,31,76,35,34,38,39,48,52,116,63,0,140,
%T A252666 68,81,66,89,96,198,97,92,415,94,0,229,119,121,539,132,133,146,292,
%U A252666 162,158,148,651,164,153,167,196,165,757,205,201,0,184,175
%N A252666 Let k be the smallest number such that s(k) = odd part of digital sum of 2^k is multiple of prime(n); then a(n)=k, if s(k) = prime(n). Otherwise, or if there is no such k, a(n)=0.
%C A252666 We conjecture that k in the definition exists for every n>=3.
%C A252666 a(n)=0 for n = 25, 37, 58, ... .
%e A252666 If n=3, evidently, k=5, since 2^5=32, s(5)= 3+2 = 5 = prime(3). So a(3)=5.
%e A252666 If n=25, then k=387, but s(387)>prime(25)=97, so a(25)=0 (the equation s(x)=97 has the smallest solution x=517).
%o A252666 (PARI) s(k) = my(sd = sumdigits(2^k)); sd/2^valuation(sd, 2);
%o A252666 a(n) = {p = prime(n); k = 1; while ((sk=s(k)) % p, k++); if (sk == p, k, 0);} \\ _Michel Marcus_, Dec 29 2014
%Y A252666 Cf. A251964, A252280, A252281, A252282, A282283.
%K A252666 nonn,base
%O A252666 3,1
%A A252666 _Vladimir Shevelev_, Dec 20 2014
%E A252666 More terms from _Peter J. C. Moses_, Dec 20 2014