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A191474 Smallest prime q such that q + prime(n) is a power of 2.

%I A191474 #28 Sep 01 2023 21:17:27
%S A191474 2,5,3,549755813881,5,3,47,13,41,3,97,2011,23,536870869,17,11,5,3,61,
%T A191474 953,439,433,173,167,31,67108763,409,149,19,911,140737488355201,16253,
%U A191474 887,373,107,2147483497,32611,349,89,83,3917,331,16193,2096959,59,313,33554221
%N A191474 Smallest prime q such that q + prime(n) is a power of 2.
%C A191474 Corresponding exponents of 2: 2, 3, 3, 39, 4, 4, 6, 5, 6, 5, 7, 11, 6, 29, 6, 6, 6, 6, 7, 10, 9, 9, 8, 8, 7, 1, 9, 8, 7, 10, 47, 14, 10, 9, 8, 31, 15, 9, 8, 8, 12, 9, 14, 21, 8, 9, 1, ...
%H A191474 Robert Israel, <a href="/A191474/b191474.txt">Table of n, a(n) for n = 1..285</a>
%e A191474 2 + 2 = 2^2,
%e A191474 3 + 5 = 2^3,
%e A191474 5 + 3 = 2^3,
%e A191474 7 + 549755813881 = 2^39,
%e A191474 11 + 5 = 2^4.
%p A191474 f:= proc(n) local p,m,t,q;
%p A191474   p:= ithprime(n);
%p A191474   for t from ilog2(p) do
%p A191474     q:= 2^t - p;
%p A191474     if isprime(q) then return q fi;
%p A191474   od;
%p A191474 end proc:
%p A191474 map(f, [$1..50]); # _Robert Israel_, Dec 23 2020
%t A191474 f[p_] := NestWhile[2 # &, 2^Ceiling[Log[2, p]], ! PrimeQ[# - p] &] - p;
%t A191474 f /@ Prime@Range@47 (* _David Trimas_, Jul 30 2023 *)
%K A191474 nonn
%O A191474 1,1
%A A191474 _Zak Seidov_, Aug 28 2012
%E A191474 a(26) corrected by _Robert Israel_, Dec 23 2020