A090793 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.

52, 80, 95, 134, 114, 141, 213, 187, 211, 274, 338, 312, 312, 292, 370, 350, 456, 486, 445, 502, 428, 465, 488, 591, 471, 540, 615, 558, 527, 513, 563, 636, 658, 659, 722, 583, 681, 789, 667, 602, 631, 632, 603, 902, 873, 626, 703, 785, 832, 670, 743, 764

Offset

1,1

Comments

Only even values of r are tested.

Links

Table of n, a(n) for n=1..52.

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.

Prog

(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", ")) ) ) }

Crossrefs

Cf. A090495 A090496.

Sequence in context: A326235 A118148 A111173 * A090791 A234099 A026067

Adjacent sequences: A090790 A090791 A090792 * A090794 A090795 A090796

Keyword

nonn

Author

Cino Hilliard, Feb 16 2004

Status

approved