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A226160

Least positive integer k such that 1 + 1/2 + ... + 1/k > n/phi, where phi = golden ratio = (1+sqrt(5))/2.

1, 2, 4, 7, 12, 23, 42, 79, 146, 271, 503, 934, 1732, 3214, 5963, 11063, 20524, 38078, 70646, 131067, 243166, 451140, 836989, 1552846, 2880960, 5344978, 9916415, 18397696, 34132822, 63325839

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OFFSET

1,2

COMMENTS

Conjecture: a(n+1)/a(n) converges to 1.8552...

Conjecture confirmed: using series expansion of HarmonicNumber(k) one gets a(n+1)/a(n) -> exp(1/phi) = 1.855276958... [Jean-François Alcover, Jun 04 2013]

LINKS

Table of n, a(n) for n=1..30.

EXAMPLE

a(4) = 7 because 1 + 1/2 + ... + 1/6 < 4*phi < 1 + 1/2 + ... + 1/7.

MATHEMATICA

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]]

CROSSREFS

Cf. A226161.

Sequence in context: A054165 A054171 A018080 * A018181 A141017 A357925

Adjacent sequences: A226157 A226158 A226159 * A226161 A226162 A226163

KEYWORD

nonn