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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.

%I A320076 #30 Nov 22 2018 02:46:05
%S A320076 1,1,2,1,1,2,32,1
%N 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.
%C A320076 a(11) > 6360.
%C A320076 a(11) > 12000. - _Chai Wah Wu_, Nov 15 2018
%C A320076 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
%C A320076 a(15) = 2590, a(23) = 3734. - _Chai Wah Wu_, Nov 21 2018
%t A320076 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 *)
%o A320076 (PARI)
%o A320076 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 A320076 Cf. A320077.
%K A320076 nonn,more
%O A320076 3,3
%A A320076 _Dmitry Ezhov_, Oct 05 2018