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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
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
FORMULA
A169628(n) = (1/2)*A171251(n) = (A000668(i) + A000668(j))/2, where n = i*(i-1)/2+j, i >= j >= 1.
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
KEYWORD
nonn
AUTHOR
M. F. Hasler, Mar 06 2010
STATUS
approved