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%I #15 Jun 04 2013 14:54:20
%S 1,2,4,7,12,23,42,79,146,271,503,934,1732,3214,5963,11063,20524,38078,
%T 70646,131067,243166,451140,836989,1552846,2880960,5344978,9916415,
%U 18397696,34132822,63325839
%N Least positive integer k such that 1 + 1/2 + ... + 1/k > n/tau, where tau = golden ratio = (1+sqrt(5))/2.
%C Conjecture: a(n+1)/a(n) converges to 1.8552...
%C 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 a(4) = 7 because 1 + 1/2 + ... + 1/6 < 4*tau < 1 + 1/2 + ... + 1/7.
%t 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 Cf. A226161.
%K nonn
%O 1,2
%A _Clark Kimberling_, May 29 2013
%E More terms from _Jean-François Alcover_, Jun 04 2013
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