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Search: id:A007703
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| A007703 |
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Regular primes.
(Formerly M2411)
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+0
5
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| 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 47, 53, 61, 71, 73, 79, 83, 89, 97, 107, 109, 113, 127, 137, 139, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 239, 241, 251, 269, 277, 281, 313, 317, 331, 337, 349, 359, 367, 373, 383, 397, 419, 431
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A prime p is regular if and only if the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) are not divisible by p.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966, pp. 425-430.
H. M. Edwards, Fermat's Last Theorem, Springer, 1977.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
C. K. Caldwell, The Prime Glossary, Regular prime
K. Conrad, Fermat's Last Theorem For Regular Primes
O. A. Ivanova, Regular prime number
D. Jao, PlanetMath.Org, Regular prime
A. L. Robledo, PlanetMath.Org, examples of regular primes
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Bernoulli numbers, irregularity index of primes
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MATHEMATICA
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s = {}; Do[p = Prime@n; k = 1; While[2k <= p - 3 && Mod[Numerator@BernoulliB[2k], p] != 0, k++ ]; If[2k > p - 3, AppendTo[s, p]], {n, 2, 80}]; s (* Robert G. Wilson v Sep 20 2006 *)
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CROSSREFS
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Cf. A000928 (irregular primes) and A061576 for further references.
Adjacent sequences: A007700 A007701 A007702 this_sequence A007704 A007705 A007706
Sequence in context: A020615 A165255 A155058 this_sequence A002556 A130101 A130057
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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Corrected by Gerard Schildberger, Jun 01, 2004
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