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%I #17 Jan 02 2023 12:30:47
%S 3,5,7,17,19,31,65,67,79,127,4097,4099,4111,4159,8191,65537,65539,
%T 65551,65599,69631,131071,262145,262147,262159,262207,266239,327679,
%U 524287,1073741825,1073741827,1073741839,1073741887,1073745919,1073807359
%N Semi-sums (average) of two (not necessarily distinct) Mersenne primes (A000668).
%C 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.
%H Vincenzo Librandi, <a href="/A169628/b169628.txt">Table of n, a(n) for n = 1..150</a>
%H Jonathan Vos Post, <a href="http://list.seqfan.eu/oldermail/seqfan/2010-March/003808.html">Sums of three Mersenne primes, and prime sums of three Mersenne primes</a>, SeqFan list, Mar 5, 2010.
%F A169628(n) = (1/2)*A171251(n) = (A000668(i) + A000668(j))/2, where n = i*(i-1)/2+j, i >= j >= 1.
%F A169628(A000217(n)) = A000668(n).
%e a(1) = (A000668(1) + A000668(1))/2,
%e a(2) = (A000668(2) + A000668(1))/2,
%e a(3) = (A000668(2) + A000668(2))/2,
%e a(4) = (A000668(3) + A000668(1))/2, ...
%t Union[Mean/@Tuples[Select[2^Prime[Range[20]]-1, PrimeQ],{2}]] (* _Harvey P. Dale_, Mar 12 2011 *)
%o (PARI) concat(vector(#A000668,i,vector(i,j,A000668[i]+A000668[j])))/2 /* having defined A000668 to be vector with initial terms of A000668 */
%Y Cf. A171253 (using only distinct terms of A000668), A171254 (primes in this sequence).
%K nonn
%O 1,1
%A _M. F. Hasler_, Mar 06 2010