%I #24 Nov 20 2018 05:26:54

%S 1,1,1,1,1,2,1,3,1,1,1,2,34,1,1,5

%N 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.

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

%C 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

%H dxdy Blog, <a href="https://dxdy.ru/topic130003.html">MSE Crusher Questioner - will anyone try?</a> (in Russian).

%H Math StackExchange, <a href="https://math.stackexchange.com/questions/2931716/is-there-are-similar-conjecture-like-this">Is there are similar conjecture like this??</a>, Sep 2018.

%t 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 *)

%o (PARI)

%o 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)))};

%Y Cf. A320076.

%K nonn,more

%O 1,6

%A _Dmitry Ezhov_, Oct 05 2018