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%I #22 Feb 21 2021 03:46:50
%S 2,3,3,4,4,4,4,5,6,5,5,5,5,5,5,7,6,6,6,6,6,29,6,6,7,6,6,6,6,6,6,8,8,7,
%T 7,10,9,7,8,7,7,8,7,7,8,7,8,10,7,7,7,7,7,8,7,7,10,7,7,7,7,7,7,47,8,8,
%U 9,8,10,9,10,8,9,8,8,9,8,8,15,8,10,9,9,8
%N Least k such that 2n+1 = 2^k - p^m for some prime p and integer m > 0, or 0 if no such k exists.
%C Since even numbers cannot be of this form unless they are powers of 2, only odd 2n+1 are considered.
%C Except for n=3, 11, 18, 19, 27, 39, 50, 51, ..., the value of k corresponds to m=1, i.e., 2^k - (2n+1) is prime.
%C a(935) >= 70000. - _Hiroaki Yamanouchi_, Nov 22 2014
%H Hiroaki Yamanouchi, <a href="/A247134/b247134.txt">Table of n, a(n) for n = 0..934</a>
%F a(n) = min{ k | exists m>1: 2n+1 = A000079(k) - A000961(m) } > log_2(n).
%o (PARI) a(n)=for(k=log(n=n*2+1)\log(2)+1,9e9,isprimepower(2^k-n)&&return(k))
%Y Cf. A000079, A000961.
%K nonn
%O 0,1
%A _M. F. Hasler_, Nov 20 2014
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