OFFSET
1,1
COMMENTS
a(n) is the least integer k for which log k > 1 + 1/2 + ... + 1/n.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A215000(n)+1.
EXAMPLE
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.
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 *)
PROG
(PARI) for(n=1, 30, print1(1 + floor(exp(sum(k=1, n, 1/k))), ", ")) \\ G. C. Greubel, Feb 01 2018
(Magma) [1 + Floor(Exp((&+[1/k :k in [1..n]]))): n in [1..30]]; // G. C. Greubel, Feb 01 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 18 2012
STATUS
approved