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A095847
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Lucas-Lehmer residues for Mersenne numbers with prime indices.
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19
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1, 0, 0, 0, 1736, 0, 0, 0, 6107895, 458738443, 0, 117093979072, 856605019673, 5774401272921, 96699253829728, 5810550306096509, 450529175803834166, 0, 44350645312365507266, 271761692158955752596, 2941647823169311845731
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OFFSET
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1,5
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COMMENTS
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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
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LINKS
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Dennis Martin, Table of n, a(n) for n = 1..100
Eric Weisstein's World of Mathematics, Lucas-Lehmer Test
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FORMULA
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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
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EXAMPLE
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The first term is 1 since 4 mod 3 = 1. - Zvi Mendlowitz (zvi113(AT)zahav.net.il), May 10 2006
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MATHEMATICA
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(* 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 *)
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CROSSREFS
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Cf. A003010.
Sequence in context: A283385 A083606 A280927 * A253696 A253703 A235014
Adjacent sequences: A095844 A095845 A095846 * A095848 A095849 A095850
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KEYWORD
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nonn
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AUTHOR
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Eric W. Weisstein, Jun 08 2004
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STATUS
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approved
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