%I #20 May 09 2018 10:46:07
%S 11,17,31,53,59,109,227,1789,3581,28669,57347,114691,229373,3670013,
%T 14680067,58720253,117440509,7516192771,60129542141,7881299347898371,
%U 264452523040700131966973,34662321099990647697175478269
%N Primes of the form 7*2^k-3 or 7*2^k+3.
%C This sequence lists the primes produced by the sum of three consecutive powers of 2 minus 3 or plus 3, 2^k+2^(k+1)+2^(k+2)+-3, generated by k = 1, 1, 2, 3, 3, 4, 5, 8, 9, 12, 13, 14, 15, 19, 21, 23, 24, 30, 33...
%C In 76 trials from k=0 to 37, 19 primes, 34 semiprimes, and 23 numbers requiring more than two different prime factors were produced. This differs from the distribution of such numbers. Starting at k=16 the final digits of the sum are the powers of 2 from 1 to 13.
%e 2^5 + 2^6 + 2^7=224, then 224-3=221=semiprime 13*17 (not contributing to the sequence) or 224+3=prime 227, an entry in the sequence.
%t lim = 100; Union[Select[7*2^Range[lim] - 3, PrimeQ], Select[7*2^Range[lim] + 3, PrimeQ]] (* _T. D. Noe_, Sep 27 2011 *)
%Y Cf. A156127, A164285.
%K nonn
%O 1,1
%A _J. M. Bergot_, Sep 27 2011
%E Entries corrected by _R. J. Mathar_, Sep 27 2011