A320077 a(n) is smallest positive integer i such that sum of numerator and denominator of sum of j^(-i), when j=1..n, is prime.

1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 34, 1, 1, 5

Offset

1,6

Comments

a(17) > 7000, a(32) = 2015.

a(18) = a(25) = a(31) = 6, a(19) = a(22) = a(37) = 5, a(20) = a(27) = a(35) = a(36) = a(39) = a(48) = 1, a(23) = a(38) = a(49) = 2, a(24) = a(29) = a(42) = 3, a(26) = 12, a(28) = 75, a(30) = 8, a(33) = 7, a(41) = 121, a(44) = 1052, a(46) = 125, a(47) = 1527. - Chai Wah Wu, Nov 19 2018

Links

Table of n, a(n) for n=1..16.

dxdy Blog, MSE Crusher Questioner - will anyone try? (in Russian).

Math StackExchange, Is there are similar conjecture like this??, Sep 2018.

Mathematica

a[n_] := Do[s = HarmonicNumber[n, r]; If[PrimeQ[Numerator[s] + Denominator[s]], Return[r]], {r, 1, Infinity}]; Table[a[n], {n, 1, 16}] (* Vaclav Kotesovec, Nov 14 2018 *)

Prog

(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)))};

Crossrefs

Cf. A320076.

Sequence in context: A333305 A110969 A362681 * A325522 A006083 A338713

Adjacent sequences: A320074 A320075 A320076 * A320078 A320079 A320080

Keyword

nonn,more

Author

Dmitry Ezhov, Oct 05 2018

Status

approved