A171254 Primes which are the average of any two (not necessarily distinct) Mersenne primes (A000668).

3, 5, 7, 17, 19, 31, 67, 79, 127, 4099, 4111, 4159, 8191, 65537, 65539, 65551, 65599, 131071, 262147, 266239, 524287, 1073741827, 1073741839, 1073807359, 2147483647, 2305843009213693951, 309485009821345068724785151

Offset: 1

Author

M. F. Hasler, Mar 06 2010

Keywords

• nonn

Comments

The subsequence of primes in A171252, containing A000668 as a subsequence.

Examples

			a(n) = A171252(n) for n=1,...,6, since all of these terms are prime. The term A171252(7) = 65 is the first element of A171252 to be composite, and therefore not included in the present sequence A171252.
		

Links

• Jonathan Vos Post, Sums of three Mersenne primes, and prime sums of three Mersenne primes, SeqFan list, Mar 5, 2010.

Crossrefs

Cf. A171252, A171255 (excludes elements of A000668).

Programs

Mathematica

Select[Mean/@Tuples[2^MersennePrimeExponent[Range[10]]-1,2],PrimeQ]//Union (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 31 2019 *)

PARI

select(isprime, concat(vector(#A00668,i,vector(i,j,A00668[i]+A00668[j])))/2) /* having defined A00668 as vector with initial terms of A000668. In PARI version 2.4.2, the syntax select( concat(...), x->isprime(x)) must be used. */

Formula

A171254 = A171252 intersect A000040.