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Lucas-Lehmer residues for Mersenne numbers with prime indices.
19

%I #20 Aug 15 2018 03:55:14

%S 1,0,0,0,1736,0,0,0,6107895,458738443,0,117093979072,856605019673,

%T 5774401272921,96699253829728,5810550306096509,450529175803834166,0,

%U 44350645312365507266,271761692158955752596,2941647823169311845731

%N Lucas-Lehmer residues for Mersenne numbers with prime indices.

%C If a(n) = 0, then 2^prime(n) - 1 is a prime greater than 3. - _Alonso del Arte_, May 09 2014

%C For n > 1, 2^prime(n) - 1 is prime if and only if a(n) = 0. - _Thomas Ordowski_, Aug 12 2018

%H Dennis Martin, <a href="/A095847/b095847.txt">Table of n, a(n) for n = 1..100</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Lucas-LehmerTest.html">Lucas-Lehmer Test</a>

%F 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

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

%t (* 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 *)

%Y Cf. A003010.

%K nonn

%O 1,5

%A _Eric W. Weisstein_, Jun 08 2004