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A004061
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Numbers k such that (5^k - 1)/4 is prime.
(Formerly M2620)
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39
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3, 7, 11, 13, 47, 127, 149, 181, 619, 929, 3407, 10949, 13241, 13873, 16519, 201359, 396413, 1888279, 3300593
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OFFSET
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1,1
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COMMENTS
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With the addition of the 19th prime in the sequence, the new best linear fit to the sequence has G=0.4723, which is slightly closer to the conjectured limit of G=0.56145948, A080130 (see link for Generalized Repunit Conjecture). [Paul Bourdelais, Apr 30 2018]
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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.
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.
Eric Weisstein's World of Mathematics, Repunit
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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hard,nonn
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AUTHOR
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EXTENSIONS
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a(13)-a(15) from Kamil Duszenko (kdusz(AT)wp.pl), Mar 25 2003
a(16) corresponds to a probable prime based on trial factoring to 4*10^13 and Fermat primality testing base 2. - Paul Bourdelais, Dec 11 2008
a(17) corresponds to a probable prime discovered by Paul Bourdelais, Jun 01 2010
a(18) corresponds to a probable prime discovered by Paul Bourdelais, Apr 30 2018
a(19) corresponds to a probable prime discovered by Ryan Propper, Jan 02 2022
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STATUS
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approved
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