A127703 Primes of the form 7*2^k-3 or 7*2^k+3.

11, 17, 31, 53, 59, 109, 227, 1789, 3581, 28669, 57347, 114691, 229373, 3670013, 14680067, 58720253, 117440509, 7516192771, 60129542141, 7881299347898371, 264452523040700131966973, 34662321099990647697175478269

Offset: 1

Author

J. M. Bergot, Sep 27 2011

Keywords

• nonn

Comments

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...

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.

Examples

			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.
		

Crossrefs

Cf. A156127, A164285.

Programs

Mathematica

lim = 100; Union[Select[7*2^Range[lim] - 3, PrimeQ], Select[7*2^Range[lim] + 3, PrimeQ]] (* T. D. Noe, Sep 27 2011 *)

Extensions

Entries corrected by R. J. Mathar, Sep 27 2011