A320076 a(n) is smallest positive integer i such that difference of numerator and denominator of sum of j^(-i), when j=1..n and n > 2, is prime.

1, 1, 2, 1, 1, 2, 32, 1

Offset: 3

Author

Dmitry Ezhov, Oct 05 2018

Keywords

• nonn
• more

Comments

a(11) > 6360.

a(11) > 12000. - Chai Wah Wu, Nov 15 2018

a(19) = a(20) = a(26) = a(30) = a(31) = a(33) = a(40) = 1, a(44) = a(48) = a(49) = 2, a(42) = 3, a(14) = 5, a(24) = a(46) = 7, a(12) = 8, a(13) = 17, a(47) = 19, a(25) = 49, a(38) = 54, a(37) = 179, a(16) = 207, a(22) = 676, a(18) = 690, a(43) = 880, a(17) = 1068, a(34) = 1199. - Chai Wah Wu, Nov 20 2018

a(15) = 2590, a(23) = 3734. - Chai Wah Wu, Nov 21 2018

Crossrefs

Cf. A320077.

Programs

Mathematica

a[n_] := Do[s = HarmonicNumber[n, r]; If[PrimeQ[Numerator[s] - Denominator[s]], Return[r]], {r, 1, Infinity}]; Table[a[n], {n, 3, 10}] (* Vaclav Kotesovec, Nov 14 2018 *)

PARI

a(n)={for(i=1, +oo, s=sum(j=1, n, j^(-i)); p=numerator(s); q=denominator(s); if(ispseudoprime(p-q), return(i)))};