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

Offset: 1

Author

Artur Jasinski, Jan 23 2006

Keywords

• nonn

Links

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

Crossrefs

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

Programs

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 *)