A045567 Numbers whose factorial has '84' as its final two digits before the trailing zeros.

25, 26, 42, 55, 103, 136, 140, 147, 158, 169, 231, 261, 265, 272, 281, 333, 344, 356, 380, 389, 410, 460, 472, 486, 503, 565, 582, 595, 598, 629, 662, 674, 677, 683, 694, 700, 701, 712, 742, 763, 777, 789, 839

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Index entries for sequences related to final digits of numbers

Mathematica

Select[Range[5, 850], Take[Flatten[Most[Split[IntegerDigits[#!]]]], -2]=={8, 4}&] (* Harvey P. Dale, Jul 02 2022 *)

Prog

(PARI) last(n, k)=if(n*8\9-1<k, n=n!; return(n/10^valuation(n, 10)%10^k)); my(m=Mod(1, 5^k)); for(i=2, n, m*=i/10^valuation(i, 5)); lift(chinese(m, Mod(0, 2^k))) \\ Gives the last k decimal digits of n!.
is(n)=last(n, 2)==84 \\ Charles R Greathouse IV, Oct 22 2014
(PARI) is(n)=my(m=Mod(1, 25)); for(i=2, n, m*=i/10^valuation(i, 5)); m==84 \\ Charles R Greathouse IV, Oct 22 2014
(PARI) v=List(); m=Mod(1, 25); for(n=2, 1e6, m*=n/10^valuation(n, 5); if(m==84, listput(v, n); if(#v==100, return(Vec(v))))) \\ Charles R Greathouse IV, Oct 22 2014

Crossrefs

Sequence in context: A349865 A195331 A175426 * A141278 A022395 A042260

Adjacent sequences: A045564 A045565 A045566 * A045568 A045569 A045570

Keyword

nonn,base

Author

Jeff Burch

Status

approved