This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A171254 #13 Dec 23 2024 14:53:42 %S A171254 3,5,7,17,19,31,67,79,127,4099,4111,4159,8191,65537,65539,65551,65599, %T A171254 131071,262147,266239,524287,1073741827,1073741839,1073807359, %U A171254 2147483647,2305843009213693951,309485009821345068724785151 %N A171254 Primes which are the average of any two (not necessarily distinct) Mersenne primes (A000668). %C A171254 The subsequence of primes in A171252, containing A000668 as a subsequence. %H A171254 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 A171254 = A171252 intersect A000040. %e A171254 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 A171254 Select[Mean/@Tuples[2^MersennePrimeExponent[Range[10]]-1,2],PrimeQ]//Union (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 31 2019 *) %o A171254 (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 A171254 Cf. A171252, A171255 (excludes elements of A000668). %K A171254 nonn %O A171254 1,1 %A A171254 _M. F. Hasler_, Mar 06 2010