A045550 Numbers whose factorial has '8' as its final nonzero digit.

9, 10, 11, 13, 15, 16, 18, 22, 27, 30, 31, 33, 39, 44, 54, 57, 70, 71, 73, 77, 80, 81, 83, 89, 94, 102, 105, 106, 108, 114, 119, 125, 126, 128, 137, 142, 149, 154, 157, 170, 171, 173, 184, 185, 186, 188, 190, 191, 193, 197, 204, 207, 220, 221, 223

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 A045549;

if n == 2 (mod 5), n+1 is in A045548;

if n == 3 (mod 5), n+1 is in A045547. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..10000 (n=1..1000 from Harvey P. Dale)

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 = 8 then count:= count+1; A[count]:= n fi;
od:
seq(A[i], i=1..100); # Robert Israel, Dec 16 2016

Mathematica

Select[Range[5, 250], Last[Flatten[Most[Split[IntegerDigits[#!]]]]]==8&] (* Harvey P. Dale, Jun 11 2014 *)
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[#] == 8 &] (* Robert G. Wilson v, Dec 28 2016 *)

Prog

(Python)
from itertools import count, islice
from functools import reduce
from sympy.ntheory.factor_ import digits
def A045550_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:8==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, 1)))
A045550_list = list(islice(A045550_gen(), 30)) # Chai Wah Wu, Dec 07 2023

Crossrefs

Cf. A008904, A045547, A045548, A045549.

Sequence in context: A253881 A097480 A034068 * A031047 A120193 A134534

Adjacent sequences: A045547 A045548 A045549 * A045551 A045552 A045553

Keyword

nonn,base

Author

Jeff Burch

Status

approved