This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A226160 #15 Jun 04 2013 14:54:20
%S A226160 1,2,4,7,12,23,42,79,146,271,503,934,1732,3214,5963,11063,20524,38078,
%T A226160 70646,131067,243166,451140,836989,1552846,2880960,5344978,9916415,
%U A226160 18397696,34132822,63325839
%N A226160 Least positive integer k such that 1 + 1/2 + ... + 1/k > n/tau, where tau = golden ratio = (1+sqrt(5))/2.
%C A226160 Conjecture: a(n+1)/a(n) converges to 1.8552...
%C A226160 Conjecture confirmed: using series expansion of HarmonicNumber(k) one gets a(n+1)/a(n) -> exp(1/tau) = 1.855276958... [_Jean-François Alcover_, Jun 04 2013]
%e A226160 a(4) = 7 because 1 + 1/2 + ... + 1/6 < 4*tau < 1 + 1/2 + ... + 1/7.
%t A226160 nn = 24; g = 1/GoldenRatio; f[n_] := 1/n; a[1] = 1; Do[s = 0; a[n] = NestWhile[# + 1 &, 1, ! (s += f[#]) > n*g &], {n, 1, nn}]; Map[a, Range[nn]]
%Y A226160 Cf. A226161.
%K A226160 nonn
%O A226160 1,2
%A A226160 _Clark Kimberling_, May 29 2013
%E A226160 More terms from _Jean-François Alcover_, Jun 04 2013