A145913 a(n) = smallest integer k such that 1/log((1 + k)^(1/k)) is bigger than n.

1, 3, 6, 10, 14, 18, 22, 27, 32, 37, 42, 47, 52, 57, 63, 68, 74, 79, 85, 91, 97, 102, 108, 114, 120, 126, 133, 139, 145, 151, 157, 164, 170, 176, 183, 189, 196, 202, 209, 216, 222, 229, 235, 242, 249, 256, 262, 269, 276, 283, 290, 297, 304, 310, 317, 324, 331

Offset

1,2

Comments

Note that 1/log((1 + k)^(1/k)) = 1/Hypergeometric2F1(1,1,2,-z).

Smallest positive integer k such that k > n*log(1 + k). - Peter Munn, Mar 21 2017

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Indranil Ghosh)

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Mar 24 2017

Mathematica

a = {}; k = 1; Do[If[N[((1/n) Log[1 + n])^(-1)] > k, AppendTo[a, n]; k = k + 1], {n, 1, 1010}]; a

Prog

(PARI) a(n) = {my(k=1); while(1, if((1/log((1 + k)^(1/k))) > n, return (k), k++)); };
for(n=1, 100, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 23 2017
(PARI) a(n)=my(k=solve(x=n*log(n), n^2, n*log(x+1)-x)\1); while(k <= n*log(k+1), k++); k \\ Charles R Greathouse IV, Mar 24 2017
(Python)
import math
def a(n):
    k=1
    while True:
        if (1/math.log((1 + k)**(1/k))) > n: return k
        else: k+=1
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Mar 23 2017

Crossrefs

Cf. A145914.

Sequence in context: A338074 A310064 A113127 * A130246 A167381 A269745

Adjacent sequences: A145910 A145911 A145912 * A145914 A145915 A145916

Keyword

nonn

Author

Artur Jasinski, Oct 24 2008

Status

approved