A215001 a(n) = 1 + floor(e^(1 + 1/2 + 1/3 + ... + 1/n)).

3, 5, 7, 9, 10, 12, 14, 16, 17, 19, 21, 23, 25, 26, 28, 30, 32, 33, 35, 37, 39, 41, 42, 44, 46, 48, 49, 51, 53, 55, 57, 58, 60, 62, 64, 66, 67, 69, 71, 73, 74, 76, 78, 80, 82, 83, 85, 87, 89, 90, 92, 94, 96, 98, 99, 101, 103, 105, 106, 108, 110, 112, 114, 115

Offset: 1

Author

Clark Kimberling, Aug 18 2012

Keywords

• nonn

Comments

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

Examples

			log 2 < 1 < log 3, so a(1) = 3;
log 4 < 1 + 1 + 1/2 < log 5, so a(2) = 5;
log 6 < 1 + 1/2 + 1/3 < log 7, so a(3) = 7.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A215000.

Programs

Magma

[1 + Floor(Exp((&+[1/k :k in [1..n]]))): n in [1..30]]; // G. C. Greubel, Feb 01 2018

Mathematica

f[n_] := Sum[1/h, {h, n}]; Table[Ceiling[E^f[n]], {n, 100}]
Floor[E^HarmonicNumber[Range[70]]]+1 (* Harvey P. Dale, Mar 04 2024 *)

PARI

for(n=1,30, print1(1 + floor(exp(sum(k=1,n,1/k))), ", ")) \\ G. C. Greubel, Feb 01 2018

Formula

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