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%I #18 Sep 04 2023 16:36:20
%S 1,2,5,129,1536,5430,13138099
%N Indices of Mersenne primes among primes of the form 24k + 7 (A107006).
%C All Mersenne primes with the exception of the first one (3) are of the form 24*k + 7.
%C Sequence lists indices m where A139483(m) is a Mersenne prime.
%e 5 is in this sequence, because A107006(5) is a Mersenne prime.
%t w = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607}; Do[w[[n]] = 2^w[[n]] - 1, {n, 1, Length[w]}]; c = 0; a = {}; Do[k = 24 n + 7; If[PrimeQ[k], c = c + 1; If[MemberQ[w, k], AppendTo[a, c]]], {n, 1, 10000000}]; a
%t With[{mps=2^#-1&/@MersennePrimeExponent[Range[20]]},Position[ Select[ 24*Range[0,10^8]+7,PrimeQ],_?(MemberQ[mps,#]&)]]//Flatten (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 20 2019 *)
%Y Cf. A107006, A124477, A139479, A139483.
%K nonn,hard,more
%O 2,2
%A _Artur Jasinski_, Apr 23 2008
%E Edited name and added example by _Dmitry Kamenetsky_, Jan 02 2011
%E a(8) from _Charles R Greathouse IV_, Mar 22 2011