A139484 Indices of Mersenne primes among primes of the form 24k + 7 (A107006).

1, 2, 5, 129, 1536, 5430, 13138099

Offset: 2

Author

Artur Jasinski, Apr 23 2008

Keywords

• nonn
• hard
• more

Comments

All Mersenne primes with the exception of the first one (3) are of the form 24*k + 7.

Sequence lists indices m where A139483(m) is a Mersenne prime.

Examples

			5 is in this sequence, because A107006(5) is a Mersenne prime.
		

Crossrefs

Cf. A107006, A124477, A139479, A139483.

Programs

Mathematica

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
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 *)

Extensions

Edited name and added example by Dmitry Kamenetsky, Jan 02 2011

a(8) from Charles R Greathouse IV, Mar 22 2011