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A226184 Least positive integer k such that 1 + 1/2 + ... + 1/n < 1/(n+1) + ... + 1/(n + k). 2
3, 9, 19, 32, 49, 69, 93, 121, 152, 187, 225, 266, 312, 361, 413, 469, 529, 592, 658, 729, 802, 880, 961, 1045, 1133, 1225, 1320, 1419, 1521, 1627, 1736, 1849, 1966, 2086, 2210, 2337, 2468, 2602, 2740, 2882, 3027, 3175, 3327, 3483, 3642, 3805, 3972, 4142 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..200

EXAMPLE

a(3) = 19 because

1/4 + 1/5 + ... + 1/(18+3) < 1 + 1/2 + 1/3 < 1/4 + 1/5 + ... + 1/(19+3)

MATHEMATICA

z = 55; f[n_] := 1/n; p[n_] := p[n] = Sum[f[k], {k, 1, n}]; Do[s = 0; a[n] = NestWhile[# + 1 &, 1, ! (s += f[#]) >= 2 p[n] &], {n, 1, z}]; m = Map[a, Range[z]]  (* A226183 *)

m1 = Table[m[[n]] - n, {n, 1, z}] (* A226184 *)

CROSSREFS

Cf. A226183.

Sequence in context: A294401 A194139 A194115 * A066506 A058331 A328950

Adjacent sequences:  A226181 A226182 A226183 * A226185 A226186 A226187

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 30 2013

STATUS

approved

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Last modified April 6 12:08 EDT 2020. Contains 333273 sequences. (Running on oeis4.)