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%I #13 Dec 23 2024 14:53:42
%S 3,5,7,17,19,31,67,79,127,4099,4111,4159,8191,65537,65539,65551,65599,
%T 131071,262147,266239,524287,1073741827,1073741839,1073807359,
%U 2147483647,2305843009213693951,309485009821345068724785151
%N Primes which are the average of any two (not necessarily distinct) Mersenne primes (A000668).
%C The subsequence of primes in A171252, containing A000668 as a subsequence.
%H Jonathan Vos Post, <a href="https://web.archive.org/web/*/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 A171254 = A171252 intersect A000040.
%e a(n) = A171252(n) for n=1,...,6, since all of these terms are prime. The term A171252(7) = 65 is the first element of A171252 to be composite, and therefore not included in the present sequence A171252.
%t Select[Mean/@Tuples[2^MersennePrimeExponent[Range[10]]-1,2],PrimeQ]//Union (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 31 2019 *)
%o (PARI) select(isprime, concat(vector(#A00668,i,vector(i,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, A171255 (excludes elements of A000668).
%K nonn
%O 1,1
%A _M. F. Hasler_, Mar 06 2010