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%I #12 Mar 14 2015 16:46:24
%S 1,3,7,13,77,182,1100,1821,9230
%N w values for A071352.
%C Some of the larger entries may only correspond to probable primes.
%C 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
%H Carlos B. Rivera F., <a href="http://www.primepuzzles.net/puzzles/puzz_223.htm">Puzzle 223</a>.
%e 2^7 = 128 is the sum of two consecutive primes (61,67), therefore 7 is a member of the sequence.
%t 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 *)
%K hard,nonn
%O 1,2
%A _Naohiro Nomoto_, May 26 2002
%E More terms from _Carlos Rivera_, Jun 07 2003
%E 9230 from _Jens Kruse Andersen_, Jun 14 2003
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