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

1,1

Comments

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

Links

Table of n, a(n) for n=1..27.

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

Formula

A171254 = A171252 intersect A000040.

Example

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.

Mathematica

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

Prog

(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. */

Crossrefs

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

Sequence in context: A045401 A085499 A169628 * A092951 A001259 A248370

Adjacent sequences: A171251 A171252 A171253 * A171255 A171256 A171257

Keyword

nonn,changed

Author

M. F. Hasler, Mar 06 2010

Status

approved