A226187 - OEIS

%I #20 Oct 06 2024 20:43:38

%S 1,1,1,2,3,4,6,8,11,16,22,31,43,60,83,116,162,227,316,441,616,859,

%T 1199,1674,2336,3260,4550,6349,8861,12367,17259,24088,33617,46916,

%U 65477,91380,127531,177984,248397,346666,483812,675214,942336,1315136,1835421,2561536,3574912,4989191,6962977,9717617

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

%C Conjecture:  a(n+1)/a(n) converges to 1.39...

%C This constant is probably exp(1/3) = 1.395612425086089528628..., see A004080. - _Ralf Stephan_, Jun 03 2013

%e a(10) = 16 because 1 + 1/2 + ... + 1/15 < 10/3 < 1 + 1/2 + ... + 1/16.

%t z = 32; f[n_] := 1/n; Do[s = 0; a[n] = NestWhile[# + 1 &, 1, ! (s += f[#]) >= n/3 &], {n, 1, z}]; m = Map[a, Range[z]]

%o (PARI) a(n)=local(s,k);s=0;k=1;while(s<=n/3,s=s+1/k;k++);k-1

%Y Cf. A226186, A226188, A002387, A004080.

%K nonn

%O 1,4

%A _Clark Kimberling_, May 30 2013

%E More terms from _Jean-François Alcover_, Jun 05 2013

%E Deleted obsolete b-file. - _N. J. A. Sloane_, Jan 04 2019