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A367799 Ordinal transform of the final nonzero digit of the factorial numbers.

%I A367799 #80 Dec 11 2023 15:27:49
%S A367799 1,2,1,1,1,2,3,2,4,1,2,3,2,4,5,5,6,3,7,6,3,4,8,5,4,6,7,9,8,5,10,11,6,
%T A367799 12,7,8,9,9,10,13,11,12,10,13,14,7,8,14,9,11,15,16,12,17,15,13,14,16,
%U A367799 15,10,11,12,18,13,16,14,15,19,16,17,17,18,17,19,20
%N A367799 Ordinal transform of the final nonzero digit of the factorial numbers.
%C A367799 n is the a(n)-th nonnegative integer producing value A008904(n).
%H A367799 Alois P. Heinz, <a href="/A367799/b367799.txt">Table of n, a(n) for n = 0..20000</a>
%F A367799 Ordinal transform of A008904.
%F A367799 a(n) = |{ j in {0..n} : A008904(j) = A008904(n) }|.
%e A367799 a(11) = 3 because 11! = 39916800 is the third factorial with final nonzero digit 8 after 9! = 362880 and 10! = 3628800. A008904(k) = 8 for k = 9, 10, 11, ... .
%o A367799 (Python)
%o A367799 from functools import reduce
%o A367799 from itertools import count, islice
%o A367799 from collections import Counter
%o A367799 from sympy.ntheory.factor_ import digits
%o A367799 def A367799_gen(): # generator of terms
%o A367799     c = Counter()
%o A367799     for n in count(0):
%o A367799         c[m:=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) if n>1 else 1]+=1
%o A367799         yield c[m]
%o A367799 A367799_list = list(islice(A367799_gen(),50)) # _Chai Wah Wu_, Dec 08 2023
%Y A367799 Cf. A000142, A004154, A008904, A368010.
%K A367799 nonn,base
%O A367799 0,2
%A A367799 _Alois P. Heinz_, Dec 07 2023