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Primes of the form 7*2^k-3 or 7*2^k+3.
0

%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