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

1,5

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

Links

Dennis Martin, Table of n, a(n) for n = 1..100

Eric Weisstein's World of Mathematics, Lucas-Lehmer Test

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

Example

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

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 *)

Crossrefs

Cf. A003010.

Sequence in context: A283385 A083606 A280927 * A253696 A253703 A235014

Adjacent sequences: A095844 A095845 A095846 * A095848 A095849 A095850

Keyword

nonn

Author

Eric W. Weisstein, Jun 08 2004

Status

approved