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A078687 Number of x>=0 such that prime(n)-2^x is prime. 6

%I

%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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Last modified June 16 14:38 EDT 2019. Contains 324152 sequences. (Running on oeis4.)