A115515 - OEIS

A115515

a(n) = largest m such that the harmonic number H(m)= Sum_{i=1..m} 1/i is < n.

0, 3, 10, 30, 82, 226, 615, 1673, 4549, 12366, 33616, 91379, 248396, 675213, 1835420, 4989190, 13562026, 36865411, 100210580, 272400599, 740461600, 2012783314, 5471312309, 14872568830, 40427833595, 109894245428

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..26.

H. P. Robinson, Letter to N. J. A. Sloane, Oct 1981

MAPLE

c:=0: H[0]:=0: for n from 1 to 10^4 do H[n]:=1/n+H[n-1]: if floor(H[n])-floor(H[n-1])=1 then c:=1+c: b[c]:=n-1: else c:=c: fi: od: seq(b[j], j=1..c); # Emeric Deutsch

MATHEMATICA

a[n_] := Ceiling[k /. FindRoot[HarmonicNumber[k] == n, {k, Exp[n]}, WorkingPrecision -> 100]] - 1;

Array[a, 26] (* Jean-François Alcover, Apr 10 2019 *)

CROSSREFS

Apart from the initial values, this is simply A002387(n)-1. Cf. A004080.

Sequence in context: A254822 A027256 A332360 * A280523 A117869 A092756

Adjacent sequences: A115512 A115513 A115514 * A115516 A115517 A115518

KEYWORD

nonn

AUTHOR

Artur Jasinski, Jan 23 2006

STATUS

approved