A008905 Leading digit of n!.

1, 1, 2, 6, 2, 1, 7, 5, 4, 3, 3, 3, 4, 6, 8, 1, 2, 3, 6, 1, 2, 5, 1, 2, 6, 1, 4, 1, 3, 8, 2, 8, 2, 8, 2, 1, 3, 1, 5, 2, 8, 3, 1, 6, 2, 1, 5, 2, 1, 6, 3, 1, 8, 4, 2, 1, 7, 4, 2, 1, 8, 5, 3, 1, 1, 8, 5, 3, 2, 1, 1, 8, 6, 4, 3, 2, 1, 1, 1, 8, 7, 5, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 1

Offset: 0

Author

Russ Cox

Keywords

• nonn
• base
• easy

Comments

Kunoff proved that the distribution of terms of this sequence follows Benford's law, i.e., the asymptotic density of terms with value d (between 1 and 9) is log_10(1+1/d). - Amiram Eldar, Sep 23 2019

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe)
• Sharon Kunoff, N! has the first digit property, The Fibonacci Quarterly, Vol. 25, No. 4 (1987), pp. 365-367.
• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A000966, A000142, A018799, A202021 (leading digit of (10^n)!), A213201.

Programs

Haskell

a008905 = a000030 . a000142  -- Reinhard Zumkeller, Apr 08 2012

Mathematica

f[n_] := Quotient[n!, 10^Floor@ Log[10, n!]]; Array[f, 105, 0]

Formula

a(n) = A000030(A000142(n)). - Reinhard Zumkeller, Apr 08 2012

Extensions

Two less-efficient Mathematica codings removed by Robert G. Wilson v, Nov 05 2010