A090800 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.

30, 42, 56, 66, 22, 20, 128, 60, 108, 82, 162, 98, 82, 18, 154, 86, 290, 278, 184, 298, 98, 172, 198, 380, 124, 238, 364, 194, 128, 92, 192, 290, 334, 336, 398, 84, 268, 484, 220, 50, 88, 90, 20, 590, 520, 18, 172, 336, 426, 78, 224, 234, 240, 552, 46, 222, 406, 500

Offset: 2

Author

Cino Hilliard, Feb 16 2004

Keywords

• nonn

Comments

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.

Crossrefs

Cf. A090495 A090496.

Programs

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",")) ) ) }

Formula

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.