A045562 Numbers whose factorial has '56' as its final two digits before the trailing zeros.

61, 96, 130, 139, 159, 161, 166, 178, 187, 192, 211, 218, 236, 255, 264, 324, 334, 341, 361, 388, 406, 432, 446, 458, 469, 483, 489, 494, 507, 537, 549, 555, 575, 576, 587, 624, 637, 654, 657, 684, 691, 697, 746, 756, 788, 793, 797, 824, 838, 840

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for sequences related to final digits of numbers

Mathematica

lnzQ[n_]:=Module[{idn=IntegerDigits[n!], lz}, lz=Length[Last[Split[idn]]]; Take[idn, {-2-lz, -1-lz}]=={5, 6}]; Select[Range[10, 850], lnzQ] (* Harvey P. Dale, Mar 05 2013 *)

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)==56 \\ 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==56 \\ 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==56, listput(v, n); if(#v==100, return(Vec(v))))) \\ Charles R Greathouse IV, Oct 22 2014

Crossrefs

Sequence in context: A309180 A038856 A144970 * A104229 A088787 A020350

Adjacent sequences: A045559 A045560 A045561 * A045563 A045564 A045565

Keyword

nonn,base

Author

Jeff Burch

Status

approved