A367799 Ordinal transform of the final nonzero digit of the factorial numbers.
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, 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, 15, 10, 11, 12, 18, 13, 16, 14, 15, 19, 16, 17, 17, 18, 17, 19, 20
Offset: 0
Examples
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, ... .
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..20000
Programs
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Python
from functools import reduce from itertools import count, islice from collections import Counter from sympy.ntheory.factor_ import digits def A367799_gen(): # generator of terms c = Counter() for n in count(0): 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 yield c[m] A367799_list = list(islice(A367799_gen(),50)) # Chai Wah Wu, Dec 08 2023
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