A045549 Numbers whose factorial has '6' as its final nonzero digit.

3, 12, 17, 24, 29, 32, 45, 46, 48, 59, 60, 61, 63, 65, 66, 68, 72, 79, 82, 95, 96, 98, 104, 107, 120, 121, 123, 127, 130, 131, 133, 139, 144, 159, 160, 161, 163, 165, 166, 168, 172, 175, 176, 178, 187, 192, 199, 209, 210, 211, 213, 215, 216, 218

Offset

1,1

Comments

From Robert Israel, Dec 16 2016: (Start)

If n is in the sequence, then:

if n == 0 (mod 5), n+1 is in the sequence;

if n == 1 (mod 5), n+1 is in A045547;

if n == 2 (mod 5), n+1 is in A045550;

if n == 3 (mod 5), n+1 is in A045548. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for sequences related to final digits of numbers

Maple

count:= 0:
r:= 1:
for n from 2 while count < 100 do
  r:= r*n;
  if r mod 10 = 0 then r:= r/10^padic:-ordp(r, 5) fi;
  if r mod 10 = 6 then count:= count+1; A[count]:= n fi;
od:
seq(A[i], i=1..100); # Robert Israel, Dec 16 2016

Mathematica

Join[{3}, Select[Range[5, 250], Most[Split[IntegerDigits[#!]]][[-1, 1]] == 6 &]] (* Vincenzo Librandi, Dec 16 2016 *)
f[n_] := Mod[6 Times @@ (Rest[ FoldList[{1 + #1[[1]], #2! 2^(#1[[1]] #2)} &, {0, 0}, Reverse[ IntegerDigits[n, 5]]]]), 10][[2]] (* after Jacob A. Siehler & Greg Dresden in A008904 *); f[0] = f[1] = 1; Select[ Range[150], f[#] == 6 &] (* Robert G. Wilson v, Dec 28 2016 *)
Select[Range[250], With[{f=#!}, Drop[IntegerDigits[f], -IntegerExponent[f]][[-1]]]==6&] (* Harvey P. Dale, Sep 27 2024 *)

Prog

(Python)
from itertools import count, islice
from functools import reduce
from sympy.ntheory.factor_ import digits
def A045549_gen(startvalue=2): # generator of terms >= startvalue
    return filter(lambda n:6==reduce(lambda x, y:x*y%10, (((6, 2, 4, 8, 6, 2, 4, 8, 2, 4, 8, 6, 6, 2, 4, 8, 4, 8, 6, 2)[(a<<2)|(i*a&3)] if i*a else (1, 1, 2, 6, 4)[a]) for i, a in enumerate(digits(n, 5)[-1:0:-1])), 6), count(max(startvalue, 2)))
A045549_list = list(islice(A045549_gen(), 30)) # Chai Wah Wu, Dec 07 2023

Crossrefs

Cf. A008904, A045547, A045548, A045550.

Sequence in context: A224924 A136047 A082965 * A103249 A354680 A047906

Adjacent sequences: A045546 A045547 A045548 * A045550 A045551 A045552

Keyword

nonn,base

Author

Jeff Burch

Status

approved