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A169628 Semi-sums (average) of two (not necessarily distinct) Mersenne primes (A000668). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 13 10:29 EST 2019. Contains 329093 sequences. (Running on oeis4.)