|
%I #10 Apr 10 2019 10:34:26
%S 0,3,10,30,82,226,615,1673,4549,12366,33616,91379,248396,675213,
%T 1835420,4989190,13562026,36865411,100210580,272400599,740461600,
%U 2012783314,5471312309,14872568830,40427833595,109894245428
%N a(n) = largest m such that the harmonic number H(m)= Sum_{i=1..m} 1/i is < n.
%H H. P. Robinson, <a href="/A006530/a006530.pdf">Letter to N. J. A. Sloane, Oct 1981</a>
%p 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_
%t a[n_] := Ceiling[k /. FindRoot[HarmonicNumber[k] == n, {k, Exp[n]}, WorkingPrecision -> 100]] - 1;
%t Array[a, 26] (* _Jean-François Alcover_, Apr 10 2019 *)
%Y Apart from the initial values, this is simply A002387(n)-1. Cf. A004080.
%K nonn
%O 1,2
%A _Artur Jasinski_, Jan 23 2006
|
