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%I #10 Jan 17 2017 08:00:54
%S 2,3,4,5,6,7,11,12,14,15,19,21,27,35,55,59,60,64,65,75,81,83,93,95,96,
%T 100,102,108,109,114,122,124,130,132,133,135,137,141,146,152,155,158,
%U 162,165,171,178,183,192,193,198,204,206,208,214,216,223,227,243,249,255,257,263,277,279,296
%N Numbers n such that the sum of the first n primes reduced by some power of 2 is prime.
%C A013916 except for the first term, 1, is a proper subset.
%C The odd terms are: 3, 5, 7, 11, 15, 19, 21, 27, 35, 55, 59, 65, 75, 81, 83, ..., .
%C The 10^k-th term: 2, 15, 469, 7980, 110374, 1359497, 16214466, 187663922, ..., .
%H Robert G. Wilson v, <a href="/A280536/b280536.txt">Table of n, a(n) for n = 1..10000</a>
%e 11 is in the sequence since the sum of the first 11 primes is A007504(11) = 160 and 160 is divisible by 2^5 which gives 5, a prime.
%t fQ[n_] := Block[{s = Sum[ Prime@ k, {k, n}]}, PrimeQ[s/2^IntegerExponent[s, 2]]]; Select[Range@300, fQ]
%Y Cf. A007504, A013916.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Jan 04 2017