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%I #4 Oct 01 2013 17:57:57
%S 52,80,95,134,114,141,213,187,211,274,338,312,312,292,370,350,456,486,
%T 445,502,428,465,488,591,471,540,615,558,527,513,563,636,658,659,722,
%U 583,681,789,667,602,631,632,603,902,873,626,703,785,832,670,743,764
%N Minimal numbers n such that numerator(Bernoulli(2*n)/(2*n)) is different from numerator(Bernoulli(2*n)/(2*n*(2*n-r))) for some integer r and the first m irregular primes including irregularity index > 1.
%C Only even values of r are tested.
%F 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 (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(n",")) ) ) }
%Y Cf. A090495 A090496.
%K nonn
%O 1,1
%A _Cino Hilliard_, Feb 16 2004