Search: id:A061576
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%I A061576
%S A061576 2,3,37,157,491,12613,78233,527377,3238481
%N A061576 Smallest prime of irregularity index n.
%C A061576 By convention 2 has irregularity index -1; regular primes (the first 
               is 3, see A007703) have index 0; an irregular prime of index n >= 
               1 is an irregular prime p (see A000928) such that p divides exactly 
               n Bernoulli numbers B_{2i} with 2i < p-1.
%D A061576 J. Buhler, R. Crandall, R. Ernvall and T. Metsankyla, Irregular primes 
               and cyclotomic invariants to four million. Math. Comp. 61 (1993), 
               no. 203, 151-153.
%D A061576 J. Buhler, R. Crandall, R. Ernvall, T. Metsankyla and M. A. Shokrollahi, 
               Irregular Primes and Cyclotomic Invariants to 12 Million, J. Symbolic 
               Computation 31, 2001, 89-96.
%D A061576 P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, 
               NY, 1995, page 326.
%H A061576 Math. Pages, <a href="http://www.mathpages.com/home/kmath411.htm">On 
               the Density of Some Exceptional Primes</a>
%H A061576 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               IrregularPrime.html">Link to a section of The World of Mathematics.</
               a>
%H A061576 <a href="Sindx_Be.html#Bernoulli">Bernoulli numbers, irregularity index 
               of primes</a>
%Y A061576 Cf. A007703, A000928.
%Y A061576 Sequence in context: A109748 A062459 A118370 this_sequence A144466 A041329 
               A060813
%Y A061576 Adjacent sequences: A061573 A061574 A061575 this_sequence A061577 A061578 
               A061579
%K A061576 nonn,nice,hard
%O A061576 -1,1
%A A061576 William G. McCallum (wmc(AT)math.arizona.edu) and Robert G. Wilson v 
               (rgwv(AT)rgwv.com), May 20 2001

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