Search: id:A073276
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%I A073276
%S A073276 37,59,67,101,103,131,149,233,257,263,271,283,293,307,311,347,389,401,
%T A073276 409,421,433,461,463,523,541,557,577,593,607,613,619,653,659,677,683,
%U A073276 727,751,757,761,773,797,811,821,827,839,877,881,887,953,971,1061,1091
%N A073276 Irregular primes (A000928) with irregularity index one.
%C A073276 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.
%C A073276 In other words, irregular primes p dividing the numerator of B(2k) for 
               a single k, 1<=k<(p-1)/2.
%D A073276 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.
%H A073276 T. D. Noe, <a href="b073276.txt">Table of n, a(n) for n=1..10000</a> 
               (from Buhler et al.)
%H A073276 <a href="Sindx_Be.html#Bernoulli">Bernoulli numbers, irregularity index 
               of primes</a>
%t A073276 Do[p = Prime[n]; k = 1; c = 0; While[ 2*k < p - 3, If[ Mod[ Numerator[ 
               BernoulliB[2*k]], p] == 0, c++ ]; k++ ]; If[ c == 1, Print[p]], {n, 
               3, 200} ]
%Y A073276 Cf. A000928, A000367, A060974, A060975 and A073277.
%Y A073276 Sequence in context: A109166 A090798 A000928 this_sequence A105460 A141851 
               A105461
%Y A073276 Adjacent sequences: A073273 A073274 A073275 this_sequence A073277 A073278 
               A073279
%K A073276 nonn
%O A073276 1,1
%A A073276 Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 22 2002

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