1,2

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 (jens.k.a(AT)get2net.dk), Oct 26 2006

Carlos B. Rivera F., Puzzle 223.

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

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}] (from Robert G. Wilson v Jan 24 2004)

Adjacent sequences: A071084 A071085 A071086 this_sequence A071088 A071089 A071090

Sequence in context: A004060 A028491 A137474 this_sequence A038691 A082718 A084741

hard,nonn

Naohiro Nomoto (n_nomoto(AT)yabumi.com), May 26 2002

More terms from Carlos B. Rivera F. (crivera(AT)primepuzzles.net), Jun 07 2003

9230 from Jens Kruse Andersen (jens.k.a(AT)get2net.dk), Jun 14 2003