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%I #7 Oct 01 2013 17:57:58
%S 30,42,56,66,22,20,128,60,108,82,162,98,82,18,154,86,290,278,184,298,
%T 98,172,198,380,124,238,364,194,128,92,192,290,334,336,398,84,268,484,
%U 220,50,88,90,20,590,520,18,172,336,426,78,224,234,240,552,46,222,406,500
%N r when numerator(Bernoulli(2*n)/(2*n)) and numerator(Bernoulli(2*n)/(2*n*(2*n-r))) are different and n is minimum for some integer r for the first i irregular primes. These include entries when the irregularity index > 1.
%C This is a generalization of the concept in A090495 and A090496. One can change the code below from p = iprime[x] to p = prime(x) and see that data for only irregular primes is generated.
%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[] or use slower PARI BIF prime() 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(r",")) ) ) }
%Y Cf. A090495 A090496.
%K nonn
%O 2,1
%A _Cino Hilliard_, Feb 16 2004
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