A065380 Primes of the form p + 2^k, p prime and k >= 0.

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 257, 263, 269, 271, 277, 281, 283, 293

Offset: 1

Author

Reinhard Zumkeller, Nov 03 2001

Keywords

• nonn

Examples

			a(3) = 11 = 3 + 2^3 = 7 + 2^2.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A010051, A000079, A065381, A156695.

Programs

Haskell

a065380 n = a065380_list !! (n-1)
a065380_list = filter f a000040_list where
   f p = any ((== 1) . a010051 . (p -)) $ takeWhile (<= p) a000079_list
-- Reinhard Zumkeller, Nov 24 2011

Mathematica

With[{upto=300},Select[Union[Select[Flatten[Outer[Plus,Prime[Range[ PrimePi[upto]]],2^Range[0,Floor[Log[2,upto]]]]],PrimeQ]],#<=upto&]] (* Harvey P. Dale, Feb 28 2012 *)

Formula

A078687(A049084(a(n))) > 0; A091932 is a subsequence. - Reinhard Zumkeller, May 07 2006