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%I #16 Jul 08 2014 00:40:28
%S 0,1,1,2,2,2,1,3,2,1,2,2,1,2,2,1,1,3,2,2,2,2,3,1,1,2,2,2,2,2,0,3,1,4,
%T 0,2,2,1,3,2,1,4,1,1,2,4,2,1,3,3,1,1,3,0,2,2,1,3,2,1,2,3,1,1,2,2,0,0,
%U 2,2,3,1,2,0,2,3,1,2,2,2,1,3,1,2,2,2,2,1,2,2,2,2,2,1,2,3,0,1,3,2,1,1,3,1,4
%N Number of x>=0 such that prime(n)-2^x is prime.
%H T. D. Noe, <a href="/A078687/b078687.txt">Table of n, a(n) for n = 1..1000</a>
%F a(A049084(A065381(n)))=0, a(A049084(A065380(n)))=1; A118953(n)<=a(n); a(n)=A109925(A000040(n)). - _Reinhard Zumkeller_, May 07 2006
%e prime(17)=59 and only 59-2^3 = 53 is prime hence a(17)=1
%t f[p_] := Block[{c = exp = 0, lmt = 1 + Floor@ Log2@ p}, While[exp < lmt, If[ PrimeQ[p - 2^exp], c++]; exp++]; c]; Array[ f@ Prime@# &, 105] (* _Robert G. Wilson v_, Jul 07 2014 *)
%o (PARI) a(n)=sum(i=0,floor(log(prime(n))/log(2)),if(isprime(prime(n)-2^i),1,0))
%Y Cf. A156695.
%K nonn
%O 1,4
%A _Benoit Cloitre_, Dec 17 2002
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