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

0,3

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A082516 A318709 A204935 * A136760 A303335 A332390

Adjacent sequences: A008902 A008903 A008904 * A008906 A008907 A008908

Keyword

nonn,base,easy

Author

Russ Cox

Extensions

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

Status

approved