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%I #10 Jan 02 2023 12:30:47
%S 5,17,19,67,79,4099,4111,4159,65537,65539,65551,65599,262147,266239,
%T 1073741827,1073741839,1073807359,309485009821345068724785151
%N Primes which are the average of two distinct Mersenne primes (A000668).
%C The subsequence of primes in A171253, which equals A171254 minus its subsequence A000668.
%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 A171255 = A171253 intersect A000040 = A171254 \ A000668.
%e a(n) = A171253(n) for n=1,2,3, since all of these terms are prime. The term A171253(4) = 65 is the first element of A171252 to be composite, and therefore not included in the present sequence A171255.
%o (PARI) select(isprime, concat(vector(#A00668,i,vector(i-1,j,A00668[i]+A00668[j])))/2) /* having defined A00668 as vector with initial terms of A000668. In PARI version 2.4.2, the syntax select( concat(...), x->isprime(x)) must be used. */
%Y Cf. A171252, A171254 (includes elements of A000668).
%K nonn
%O 1,1
%A _M. F. Hasler_, Mar 06 2010