A356861 a(n) is the number of nonzero digits in the product of the first n numbers not divisible by 5.

1, 1, 1, 1, 2, 3, 2, 3, 5, 6, 5, 8, 10, 10, 11, 12, 15, 14, 16, 19, 20, 20, 19, 23, 24, 25, 27, 24, 27, 31, 32, 32, 34, 38, 36, 40, 41, 40, 44, 47, 43, 50, 52, 53, 50, 51, 56, 61, 60, 58, 63, 61, 64, 67, 72, 67, 70, 72, 76, 72, 78, 84, 83, 85, 84, 90, 91, 91, 90

Offset: 0

Author

Stefano Spezia, Sep 01 2022

Keywords

• nonn
• base

Crossrefs

Cf. A047201, A055640, A356858.

Cf. A356859 (number of zero digits), A356860 (number of digits).

Programs

Mathematica

Table[Length[Select[IntegerDigits[Product[Floor[(5i-1)/4], {i,n}]], Positive]], {n,0,68}]

Python

from math import prod
def a(n): s = str(prod((5*k-1)//4 for k in range(1, n+1))); return len(s) - s.count("0")
print([a(n) for n in range(69)]) # Michael S. Branicky, Sep 01 2022

Formula

a(n) = A055640(A356858(n)).