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

Author

M. F. Hasler, Mar 06 2010

Keywords

• nonn

Comments

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

Examples

			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, ...
		

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.

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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

a(A000217(n)) = A000668(n).