A095847 Lucas-Lehmer residues for Mersenne numbers with prime indices.

1, 0, 0, 0, 1736, 0, 0, 0, 6107895, 458738443, 0, 117093979072, 856605019673, 5774401272921, 96699253829728, 5810550306096509, 450529175803834166, 0, 44350645312365507266, 271761692158955752596, 2941647823169311845731

Offset: 1

Author

Eric W. Weisstein, Jun 08 2004

Keywords

• nonn

Comments

If a(n) = 0, then 2^prime(n) - 1 is a prime greater than 3. - Alonso del Arte, May 09 2014

For n > 1, 2^prime(n) - 1 is prime if and only if a(n) = 0. - Thomas Ordowski, Aug 12 2018

Examples

			The first term is 1 since 4 mod 3 = 1. - Zvi Mendlowitz (zvi113(AT)zahav.net.il), May 10 2006
		

Links

• Dennis Martin, Table of n, a(n) for n = 1..100
• Eric Weisstein's World of Mathematics, Lucas-Lehmer Test

Crossrefs

Cf. A003010.

Programs

Mathematica

(* First run the program for A003010 to define seqLucasLehmer *) Table[Mod[seqLucasLehmer[Prime[n] - 2], 2^Prime[n] - 1], {n, 20}] (* Alonso del Arte, May 09 2014 *)

Formula

First, s(0) = 4, s(i) = s(i - 1)^2 - 2. Then, a(n) = s(prime(n) - 2) mod 2^prime(n) - 1. - Alonso del Arte, May 09 2014