A202021 The leading digit of (10^n)!.

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

Offset: 0

Author

Robert G. Wilson v, Jan 09 2013

Keywords

• nonn
• base

Comments

I employed R. Wm. Gosper's approximation (A090583).

Examples

			(10^1)! = 3628800 begins with 3.
(10^6)! begins with 8 and (10^100)! begins with 1.
		

Links

• Google-tm Answers, mathtalk-ga on Apr 16 2005 19:20 PDT
• Eric Weisstein's World of Mathematics, Stirling's Approximation.

Crossrefs

Cf. A008905, A132826.

Programs

Mathematica

f[n_] := IntegerPart[ 10^FractionalPart[ N[(n*Log[n] - n + (1/2) Log[2 Pi*n + 1/3])/Log[10], 150]]]; f[1] = 1; Table[ f[10^n], {n, 0, 104}]

PARI

a(n)=my(g=lngamma(10^n+1)/log(10));g-=g\1;10^g\1 \\ Charles R Greathouse IV, Jan 09 2013