A114467 Number of decimal digits in the numerator of the 10^n-th harmonic number.

1, 4, 41, 434, 4346, 43451, 434111, 4342303, 43428680

Offset: 0

Author

Eric W. Weisstein, Nov 29 2005

Keywords

• nonn
• base
• more

Comments

See A114468 for denominators.

Eric Weisstein's link conjectures that for both this sequence and A114468, a(n) ~ (log_10(e) = A002285)*10^n. - Natalia L. Skirrow, Jun 22 2023

Links

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

Crossrefs

Cf. A001008, A002285, A002805, A114468.

Programs

Mathematica

Table[IntegerLength[Numerator[HarmonicNumber[10^n]]],{n,0,8}](* Harvey P. Dale, May 24 2019 *)

Python

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

Extensions

Edited by Charles R Greathouse IV, Aug 05 2010