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A202021 The leading digit of (10^n)!. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..104.

Google-tm Answers, mathtalk-ga on Apr 16 2005 19:20 PDT

Eric Weisstein's World of Mathematics, Stirling's Approximation, Section in World of Mathematics.

EXAMPLE

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

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}]

PROG

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

CROSSREFS

Cf. A008905, A132826.

Sequence in context: A125143 A200012 A130701 * A197507 A264992 A050000

Adjacent sequences:  A202018 A202019 A202020 * A202022 A202023 A202024

KEYWORD

nonn,base

AUTHOR

Robert G. Wilson v, Jan 09 2013

STATUS

approved

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)