%I A090798
%S A090798 37,59,67,101,103,131,149,157,157,233,257,263,271,283,293,307,311,347,
%T A090798 353,353,379,379,389,401,409,421,433,461,463,467,467,491,491,491,523,
%U A090798 541,547,547,557,577,587,587,593,607,613,617,617,617,619,631,631,647
%N A090798 Irregular primes in the ratio numerator(Bernoulli(2*n)/(2*n)) / numerator(Bernoulli(2*n)/
               (2*n*(2*n-r))) when these numerators are different and n is a minimum 
               for some integer r. Duplication indicates irregularity index > 1.
%C A090798 Only even values of r are tested.
%F A090798 Given a = numerator(Bernoulli(2*n)/(2*n)) and b = numerator(a/(2*n-r)) 
               for integer r positive or negative, then n>0 n = p + r/2 For every 
               irregular prime p there is an r such that n is minimum.
%o A090798 (PARI) \ prestore some ireg primes in iprime[] bernmin(m) = { for(x=1,
               m, p=iprime[x]; forstep(r=2,p,2, n=r/2+p; n2=n+n; a = numerator(bernfrac(n2)/
               (n2)); \ A001067 b = numerator(a/(n2-r)); \ if(a <> b,print(r","n",
               "a/b)) if(a <> b,print1(a/b",")) ) ) }
%Y A090798 Cf. A090495 A090496.
%Y A090798 Sequence in context: A134222 A127023 A109166 this_sequence A000928 A073276 
               A105460
%Y A090798 Adjacent sequences: A090795 A090796 A090797 this_sequence A090799 A090800 
               A090801
%K A090798 nonn
%O A090798 1,1
%A A090798 Cino Hilliard (hillcino368(AT)gmail.com), Feb 16 2004