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
Keywords
Programs
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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",")) ) ) }
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.
Comments