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A002184
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a(n) = least primitive factor of 2^(2n+1) - 1.
(Formerly M4400 N1855)
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4
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1, 7, 31, 127, 73, 23, 8191, 151, 131071, 524287, 337, 47, 601, 262657, 233, 2147483647, 599479, 71, 223, 79, 13367, 431, 631, 2351, 4432676798593, 103, 6361, 881, 32377, 179951, 2305843009213693951, 92737, 145295143558111, 193707721, 10052678938039, 228479, 439, 100801, 581283643249112959, 2687, 2593, 167
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OFFSET
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0,2
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COMMENTS
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For n > 0, 2^(a(n)-2n-2) == 1 (mod a(n)), since 2^(a(n)-1) == 2^(2n+1) == 1 (mod a(n)). - Thomas Ordowski, Aug 11 2021
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REFERENCES
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J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 2, p. 84.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
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FORMULA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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