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%I A320077 #24 Nov 20 2018 05:26:54
%S A320077 1,1,1,1,1,2,1,3,1,1,1,2,34,1,1,5
%N 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.
%C A320077 a(17) > 7000, a(32) = 2015.
%C A320077 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 A320077 dxdy Blog, <a href="https://dxdy.ru/topic130003.html">MSE Crusher Questioner - will anyone try?</a> (in Russian).
%H A320077 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 A320077 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 A320077 (PARI)
%o A320077 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 A320077 Cf. A320076.
%K A320077 nonn,more
%O A320077 1,6
%A A320077 _Dmitry Ezhov_, Oct 05 2018

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