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A000976 Period of 1 / n! in base 10. 3
0, 0, 1, 1, 1, 1, 6, 6, 18, 18, 18, 54, 54, 378, 1134, 1134, 9072, 81648, 81648, 81648, 1714608, 18860688, 18860688, 56582064, 56582064, 735566832, 19860304464, 139022131248, 139022131248, 417066393744, 2085331968720, 2085331968720, 68815954967760 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Formula and program of C. Ronaldo only works for n<25, because they do not remove enough powers of 5 for n>=25. - Sean A. Irvine, Sep 29 2011

LINKS

T. D. Noe, Table of n, a(n) for n = 1..200

FORMULA

a(n) = k where k is the smallest integer>=1 such that 10^k=1 mod n!/(2^A011371(n)*5^floor(n/5)) and A011371 is the highest power of 2 dividing n!. - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 16 2004

a(n) = order(10, n!/(2^s*5^t)) where 2^s is largest power of 2 dividing n! and 5^t is largest power of 5 dividing n! - Sean A. Irvine, Sep 29 2011

MAPLE

with(numtheory): Digits:=100: A011371:= proc(n) options remember: if n=0 then RETURN(0) else RETURN(A011371(floor(n/2))+floor(n/2)) fi: end; A000976:= proc(n) RETURN(order(10, n!/(2^A011371(n)*5^floor(n/5)))): end; 0, 0, seq(A000976(n), n=3..24); (C. Ronaldo)

MATHEMATICA

Join[{0, 0}, Table[num = n!/(2^IntegerExponent[n!, 2] * 5^IntegerExponent[n!, 5]); MultiplicativeOrder[10, num], {n, 3, 30}]] (* T. D. Noe, Jun 21 2012 *)

CROSSREFS

Sequence in context: A315818 A315819 A301682 * A315820 A315821 A315822

Adjacent sequences:  A000973 A000974 A000975 * A000977 A000978 A000979

KEYWORD

nonn,base

AUTHOR

Simon Plouffe

EXTENSIONS

One more term from Sean A. Irvine, Sep 28 2011

STATUS

approved

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Last modified June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)