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

0,2

Comments

n is the a(n)-th nonnegative integer producing value A008904(n).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Formula

Ordinal transform of A008904.

a(n) = |{ j in {0..n} : A008904(j) = A008904(n) }|.

Example

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, ... .

Prog

(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

Crossrefs

Cf. A000142, A004154, A008904, A368010.

Sequence in context: A316854 A367759 A125769 * A272084 A003023 A156070

Adjacent sequences: A367796 A367797 A367798 * A367800 A367801 A367802

Keyword

nonn,base

Author

Alois P. Heinz, Dec 07 2023

Status

approved