A215001 - OEIS

%I #13 Mar 04 2024 16:37:30

%S 3,5,7,9,10,12,14,16,17,19,21,23,25,26,28,30,32,33,35,37,39,41,42,44,

%T 46,48,49,51,53,55,57,58,60,62,64,66,67,69,71,73,74,76,78,80,82,83,85,

%U 87,89,90,92,94,96,98,99,101,103,105,106,108,110,112,114,115

%N a(n) = 1 + floor(e^(1 + 1/2 + 1/3 + ... + 1/n)).

%C a(n) is the least integer k for which log k > 1 + 1/2 + ... + 1/n.

%H Clark Kimberling, <a href="/A215001/b215001.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A215000(n)+1.

%e log 2 < 1 < log 3, so a(1) = 3;

%e log 4 < 1 + 1 + 1/2 < log 5, so a(2) = 5;

%e log 6 < 1 + 1/2 + 1/3 < log 7, so a(3) = 7.

%t f[n_] := Sum[1/h, {h, n}]; Table[Ceiling[E^f[n]], {n, 100}]

%t Floor[E^HarmonicNumber[Range[70]]]+1 (* _Harvey P. Dale_, Mar 04 2024 *)

%o (PARI) for(n=1,30, print1(1 + floor(exp(sum(k=1,n,1/k))), ", ")) \\ _G. C. Greubel_, Feb 01 2018

%o (Magma) [1 + Floor(Exp((&+[1/k :k in [1..n]]))): n in [1..30]]; // _G. C. Greubel_, Feb 01 2018

%Y Cf. A215000.

%K nonn

%O 1,1

%A _Clark Kimberling_, Aug 18 2012