A045554 Numbers whose factorial has '16' as its final two digits before the trailing zeros.

12, 29, 32, 59, 66, 72, 121, 133, 144, 165, 243, 258, 269, 288, 293, 297, 338, 340, 368, 384, 385, 391, 402, 414, 464, 521, 552, 558, 569, 592, 599, 612, 625, 626, 670, 673, 690, 704, 732, 785, 835, 847, 860, 865, 880, 889, 949, 959, 966, 986, 1018, 1080, 1102

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

f2nzdQ[n_]:=Module[{nf=n!}, Mod[nf/10^IntegerExponent[nf], 100]==16]; Select[ Range[1000], f2nzdQ] (* Harvey P. Dale, May 28 2015 *)

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)==16 \\ 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==16 \\ 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==16, listput(v, n); if(#v==100, return(Vec(v))))) \\ Charles R Greathouse IV, Oct 22 2014
(Python)
from math import factorial
def ok(n): return str(factorial(n)).rstrip("0").endswith("16")
print([k for k in range(1103) if ok(k)]) # Michael S. Branicky, Dec 29 2021

Crossrefs

Cf. A000142 (factorial).

Sequence in context: A189539 A000546 A130516 * A174649 A161452 A353872

Adjacent sequences: A045551 A045552 A045553 * A045555 A045556 A045557

Keyword

nonn,base

Author

Jeff Burch

Status

approved