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

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, 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, 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

Offset

1,4

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Formula

a(A049084(A065381(n)))=0, a(A049084(A065380(n)))=1; A118953(n)<=a(n); a(n)=A109925(A000040(n)). - Reinhard Zumkeller, May 07 2006

Example

prime(17)=59 and only 59-2^3 = 53 is prime hence a(17)=1

Mathematica

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 *)

Prog

(PARI) a(n)=sum(i=0, floor(log(prime(n))/log(2)), if(isprime(prime(n)-2^i), 1, 0))

Crossrefs

Cf. A156695.

Sequence in context: A340967 A230243 A338898 * A133138 A348193 A194326

Adjacent sequences: A078684 A078685 A078686 * A078688 A078689 A078690

Keyword

nonn

Author

Benoit Cloitre, Dec 17 2002

Status

approved