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A095847
Lucas-Lehmer residues for Mersenne numbers with prime indices.
19
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
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
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jun 08 2004
STATUS
approved