A045561 - OEIS

A045561

Numbers whose factorial has '52' as its final two digits before the trailing zeros.

34, 36, 41, 86, 93, 122, 132, 150, 151, 167, 177, 183, 194, 249, 257, 342, 349, 374, 399, 421, 440, 479, 511, 515, 522, 557, 571, 580, 606, 631, 665, 678, 687, 692, 734, 738, 741, 754, 778, 867, 895, 898, 912, 924, 931, 939, 950, 951, 962, 975, 976, 1012

(list; graph; refs; listen; history; text; internal format)

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, 1100], Take[Flatten[Most[Split[IntegerDigits[#!]]]], -2] == {5, 2}&] (* Harvey P. Dale, Aug 08 2016 *)

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)==52 \\ 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==52 && n>2 \\ Charles R Greathouse IV, Oct 22 2014

(PARI) v=List(); m=Mod(6, 25); for(n=4, 1e6, m*=n/10^valuation(n, 5); if(m==52, listput(v, n); if(#v==100, return(Vec(v))))) \\ Charles R Greathouse IV, Oct 22 2014

CROSSREFS

Sequence in context: A203462 A270311 A257315 * A294282 A067190 A306119

Adjacent sequences: A045558 A045559 A045560 * A045562 A045563 A045564

KEYWORD

nonn,base

AUTHOR

Jeff Burch

EXTENSIONS

More terms from Robert G. Wilson v, Dec 14 2000

STATUS

approved