cp's OEIS Frontend

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.

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A226188 Least positive integer k such that 1 + 1/2 + ... + 1/k > 2n/3.

Original entry on oeis.org

1, 2, 4, 8, 16, 31, 60, 116, 227, 441, 859, 1674, 3260, 6349, 12367, 24088, 46916, 91380, 177984, 346666, 675214, 1315136, 2561536, 4989191, 9717617, 18927334, 36865412
Offset: 1

Views

Author

Clark Kimberling, May 30 2013

Keywords

Comments

Conjecture: a(n+1)/a(n) converges to 1.94...
Conjecture confirmed: series expansion of HarmonicNumber(k) gives a(n+1)/a(n) -> exp(2/3) = 1.947734... [Jean-François Alcover, Jun 05 2013]

Examples

			a(8) = 116 because 1 + 1/2 + ... + 1/115 < 16/3 < 1 + 1/2 + ... + 1/116.

Crossrefs

Cf. A226186, A226187.

Programs

  • Mathematica
    z = 18; f[n_] := 1/n; Do[s = 0; a[n] = NestWhile[# + 1 &, 1, ! (s += f[#]) >= 2n/3 &], {n, 1, z}]; m = Map[a, Range[z]]

Extensions

More terms from Jean-François Alcover, Jun 05 2013
Deleted obsolete b-file. - N. J. A. Sloane, Jan 04 2019
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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