A169628 Semi-sums (average) of two (not necessarily distinct) Mersenne primes (A000668).

3, 5, 7, 17, 19, 31, 65, 67, 79, 127, 4097, 4099, 4111, 4159, 8191, 65537, 65539, 65551, 65599, 69631, 131071, 262145, 262147, 262159, 262207, 266239, 327679, 524287, 1073741825, 1073741827, 1073741839, 1073741887, 1073745919, 1073807359

Offset

1,1

Comments

Since all terms of A000668 are odd, the semi-sum of any two terms is integer. This motivated introduction of this sequence, A169628 = 1/2 * A171251, see there for further information.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..150

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

Formula

A169628(n) = (1/2)*A171251(n) = (A000668(i) + A000668(j))/2, where n = i*(i-1)/2+j, i >= j >= 1.

A169628(A000217(n)) = A000668(n).

Example

a(1) = (A000668(1) + A000668(1))/2,
a(2) = (A000668(2) + A000668(1))/2,
a(3) = (A000668(2) + A000668(2))/2,
a(4) = (A000668(3) + A000668(1))/2, ...

Mathematica

Union[Mean/@Tuples[Select[2^Prime[Range[20]]-1, PrimeQ], {2}]]  (* Harvey P. Dale, Mar 12 2011 *)

Prog

(PARI) concat(vector(#A000668, i, vector(i, j, A000668[i]+A000668[j])))/2 /* having defined A000668 to be vector with initial terms of A000668 */

Crossrefs

Cf. A171253 (using only distinct terms of A000668), A171254 (primes in this sequence).

Sequence in context: A122395 A045401 A085499 * A171254 A092951 A001259

Adjacent sequences: A169625 A169626 A169627 * A169629 A169630 A169631

Keyword

nonn

Author

M. F. Hasler, Mar 06 2010

Status

approved