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Number of decimal digits in the denominator of the 10^n-th harmonic number.
2

%I #19 Jun 23 2023 02:08:44

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

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

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

%H J. Sondow and E. W. Weisstein, <a href="http://mathworld.wolfram.com/HarmonicNumber.html">MathWorld: Harmonic Number</a>

%o (Python)

%o from gmpy2 import digits, mpq

%o def a(n): return len(digits(sum(mpq(1, n) for n in range(1, 10**n+1)).denominator))

%o print([a(n) for n in range(6)]) # _Michael S. Branicky_, Jun 22 2023

%Y Cf. A001008, A002805, A114467.

%K nonn,base,more

%O 0,2

%A _Eric W. Weisstein_, Nov 29 2005

%E Edited by _Charles R Greathouse IV_, Aug 05 2010