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%I #58 Aug 16 2022 16:06:24
%S 1,2,2,4,4,6,6,7,0,8,6,12,8,12,10,16,0,18,18,18,12,10,16,21,0,15,22,
%T 22,0,30,20,24,0,32,34,21,8,3,38,36,16,26,0,43,0,43,42,43,0,48,46,38,
%U 0,28,44,55,0,54,0,60,56,28,56,60,64,63,48,60,0
%N Greatest k <= n such that 2^n+2^k-1 is prime, or 0 if no such k exists.
%C Up to n=6600, a(n) = 0 for 867 values of n and a(n) >= n/2 for 4931 values of n.
%C When n+1 is a prime in A000043 and k=n, then 2^n+2^k-1 = 2^(n+1)-1 is a Mersenne Prime.
%H Pierre CAMI, <a href="/A179291/b179291.txt">Table of n, a(n) for n = 1..10000</a>
%t Table[k=n; While[k>0 && ! PrimeQ[2^n+2^k-1], k--]; k, {n, 100}] (* _T. D. Noe_, Jan 12 2011 *)
%o (PARI) A179291(n)={forstep(i=n,1,-1,if(isprime(2^n+2^i-1),return(i)));return(0)} \\ _Michael B. Porter_, Jan 12 2011
%Y Cf. A106821, A178993, A179013, A179760, A181498, A181514, A181408, A181409.
%K nonn
%O 1,2
%A _Pierre CAMI_, Jan 12 2011
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