A114468 Number of decimal digits in the denominator of the 10^n-th harmonic number.

1, 4, 40, 433, 4345, 43450, 434110, 4342302, 43428678

Offset

0,2

Comments

These numbers converge to the decimal expansion of log_10(e) = 0.43429448...

Links

Table of n, a(n) for n=0..8.

J. Sondow and E. W. Weisstein, MathWorld: Harmonic Number

Prog

(Python)
from gmpy2 import digits, mpq
def a(n): return len(digits(sum(mpq(1, n) for n in range(1, 10**n+1)).denominator))
print([a(n) for n in range(6)]) # Michael S. Branicky, Jun 22 2023

Crossrefs

Cf. A001008, A002805, A114467.

Sequence in context: A220965 A278036 A221588 * A264112 A372460 A304447

Adjacent sequences: A114465 A114466 A114467 * A114469 A114470 A114471

Keyword

nonn,base,more

Author

Eric W. Weisstein, Nov 29 2005

Extensions

Edited by Charles R Greathouse IV, Aug 05 2010

Status

approved