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A045549
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Numbers whose factorial has '6' as its final nonzero digit.
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6
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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
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OFFSET
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1,1
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COMMENTS
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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)
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LINKS
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(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)))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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