A071087 w values for A071352.

1, 3, 7, 13, 77, 182, 1100, 1821, 9230

Offset: 1

Author

Naohiro Nomoto, May 26 2002

Keywords

• hard
• nonn

Comments

Some of the larger entries may only correspond to probable primes.

For n>1, a(n) are numbers x such that 2^x is the sum of two consecutive primes. 2^(x-1) is the average of those primes. For a(2) to a(9) the primes are: 2^2+/-1 = (3,5), 2^6+/-3 = (61,67), 2^12+/-3 = (4093,4099), 2^76+/-15, 2^181+/-165, 2^1099+/-1035, 2^1820+/-663, 2^9229+/-2211. - Jens Kruse Andersen, Oct 26 2006

Examples

			2^7 = 128 is the sum of two consecutive primes (61,67), therefore 7 is a member of the sequence.
		

Links

• Carlos B. Rivera F., Puzzle 223.

Programs

Mathematica

PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; Do[ p = PrevPrim[2^n]; q = NextPrim[2^n]; If[p + q == 2^(n + 1), Print[n+1]], {n, 2, 9230}] (* Robert G. Wilson v, Jan 24 2004 *)

Extensions

More terms from Carlos Rivera, Jun 07 2003

9230 from Jens Kruse Andersen, Jun 14 2003