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

%I A045549 #36 Sep 27 2024 14:00:35
%S A045549 3,12,17,24,29,32,45,46,48,59,60,61,63,65,66,68,72,79,82,95,96,98,104,
%T A045549 107,120,121,123,127,130,131,133,139,144,159,160,161,163,165,166,168,
%U A045549 172,175,176,178,187,192,199,209,210,211,213,215,216,218
%N A045549 Numbers whose factorial has '6' as its final nonzero digit.
%C A045549 From _Robert Israel_, Dec 16 2016: (Start)
%C A045549 If n is in the sequence, then:
%C A045549 if n == 0 (mod 5), n+1 is in the sequence;
%C A045549 if n == 1 (mod 5), n+1 is in A045547;
%C A045549 if n == 2 (mod 5), n+1 is in A045550;
%C A045549 if n == 3 (mod 5), n+1 is in A045548. (End)
%H A045549 Robert Israel, <a href="/A045549/b045549.txt">Table of n, a(n) for n = 1..10000</a>
%H A045549 <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>
%p A045549 count:= 0:
%p A045549 r:= 1:
%p A045549 for n from 2 while count < 100 do
%p A045549   r:= r*n;
%p A045549   if r mod 10 = 0 then r:= r/10^padic:-ordp(r,5) fi;
%p A045549   if r mod 10 = 6 then count:= count+1; A[count]:= n fi;
%p A045549 od:
%p A045549 seq(A[i],i=1..100); # _Robert Israel_, Dec 16 2016
%t A045549 Join[{3}, Select[Range[5,250], Most[Split[IntegerDigits[#!]]][[-1, 1]] == 6 &]] (* _Vincenzo Librandi_, Dec 16 2016 *)
%t A045549 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 *)
%t A045549 Select[Range[250],With[{f=#!},Drop[IntegerDigits[f],-IntegerExponent[f]][[-1]]]==6&] (* _Harvey P. Dale_, Sep 27 2024 *)
%o A045549 (Python)
%o A045549 from itertools import count, islice
%o A045549 from functools import reduce
%o A045549 from sympy.ntheory.factor_ import digits
%o A045549 def A045549_gen(startvalue=2): # generator of terms >= startvalue
%o A045549     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)))
%o A045549 A045549_list = list(islice(A045549_gen(),30)) # _Chai Wah Wu_, Dec 07 2023
%Y A045549 Cf. A008904, A045547, A045548, A045550.
%K A045549 nonn,base
%O A045549 1,1
%A A045549 _Jeff Burch_