Search: id:A007703
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%I A007703 M2411
%S A007703 3,5,7,11,13,17,19,23,29,31,41,43,47,53,61,71,73,79,83,89,97,107,109,
%T A007703 113,127,137,139,151,163,167,173,179,181,191,193,197,199,211,223,227,229,
%U A007703 239,241,251,269,277,281,313,317,331,337,349,359,367,373,383,397,419,431
%N A007703 Regular primes.
%C A007703 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.
%D A007703 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007703 Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, 
               NY, 1966, pp. 425-430.
%D A007703 H. M. Edwards, Fermat's Last Theorem, Springer, 1977.
%H A007703 T. D. Noe, <a href="b007703.txt">Table of n, a(n) for n = 1..10000</a>
%H A007703 C. K. Caldwell, The Prime Glossary, <a href="http://primes.utm.edu/glossary/
               page.php/Regular.html">Regular prime</a>
%H A007703 K. Conrad, <a href="http://www.math.uconn.edu/~kconrad/blurbs/fltreg.pdf">
               Fermat's Last Theorem For Regular Primes</a>
%H A007703 O. A. Ivanova, <a href="http://eom.springer.de/R/r080800.htm">Regular 
               prime number</a>
%H A007703 D. Jao, PlanetMath.Org, <a href="http://planetmath.org/encyclopedia/RegularPrime.html">
               Regular prime</a>
%H A007703 A. L. Robledo, PlanetMath.Org, <a href="http://planetmath.org/encyclopedia/
               ExampleOfRegularPrime.html">examples of regular primes</a>
%H A007703 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               RegularPrime.html">Link to a section of The World of Mathematics.</
               a>
%H A007703 <a href="Sindx_Be.html#Bernoulli">Bernoulli numbers, irregularity index 
               of primes</a>
%t A007703 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 *)
%Y A007703 Cf. A000928 (irregular primes) and A061576 for further references.
%Y A007703 Sequence in context: A020615 A165255 A155058 this_sequence A002556 A130101 
               A130057
%Y A007703 Adjacent sequences: A007700 A007701 A007702 this_sequence A007704 A007705 
               A007706
%K A007703 nonn,nice
%O A007703 1,1
%A A007703 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A007703 Corrected by Gerard Schildberger, Jun 01, 2004

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