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A018799 Smallest nonnegative integer m such that m! begins with n in base 10. 13
0, 2, 9, 8, 7, 3, 6, 14, 96, 27, 22, 5, 15, 42, 25, 89, 69, 76, 63, 16, 87, 113, 54, 4, 23, 30, 205, 85, 34, 28, 62, 164, 41, 245, 17, 9, 36, 128, 11, 8, 185, 53, 351, 73, 369, 118, 12, 265, 129, 7, 21, 38, 235, 66, 46, 258, 81, 597, 279, 43, 72, 13, 559, 18, 203, 120, 311 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Record high values are m = 0, 2, 9, 14, 96, 113, 205, 245, 351, 369, 597, ... (see A279089); these occur, respectively, at n = 1, 2, 3, 8, 9, 22, 27, 34, 43, 45, 58, ... (see A279090). - Jon E. Schoenfield, Jan 30 2017

The existence of such m for each n was proven by Maxfield in 1970. The first 999 terms of this sequence were calculated by Southard in 1983. - Amiram Eldar, Dec 18 2018

LINKS

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (terms 1..1000 from David W. Wilson).

John E. Maxfield, A Note on N!, Mathematics Magazine, Vol. 43. No. 2 (1970), pp. 64-67.

Laura Southard, Investigations on Maxfield's Theorem, Pi Mu Epsilon Journal, Vol. 7, No. 8 (1983), pp. 493-495, alternative link.

EXAMPLE

Since no factorial below 96! ~ 9.91*10^149 starts with 9, we have a(9) = 96. Similarly, 16 first appears as the leading digits of 89! ~ 1.65*10^136 and hence a(16) = 89. - Lekraj Beedassy, Oct 31 2010 and Robert G. Wilson v, Nov 05 2010

MATHEMATICA

f[n_] := Block[{k = 0, m}, While[ m = Max[0, Floor@ Log[10, k! ] - Floor@ Log[10, n]]; (k! - Mod[k!, 10^m])/10^m != n, k++ ]; k]; Array[f, 67] (* Robert G. Wilson v, Nov 05 2010 *)

PROG

(PARI) A018799(n)={ local( F=1, k=0 ); while( F\1!=n, F*=k++; while( F>=n+1, F/=10)); k} \\ M. F. Hasler, Feb 01 2009

CROSSREFS

Cf. A018854.

Apart from leading term, identical to A076219.

Cf. A000142, A008905, A279089, A279090.

Sequence in context: A021975 A192599 A021081 * A076219 A077601 A090930

Adjacent sequences:  A018796 A018797 A018798 * A018800 A018801 A018802

KEYWORD

nonn,base

AUTHOR

David W. Wilson

STATUS

approved

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Last modified November 12 17:06 EST 2019. Contains 329058 sequences. (Running on oeis4.)