A356859 a(n) is the number of zero digits in the product of the first n numbers not divisible by 5.

0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2, 1, 0, 1, 1, 1, 0, 2, 1, 0, 0, 2, 4, 1, 2, 2, 2, 6, 5, 2, 3, 5, 4, 2, 5, 3, 4, 6, 4, 3, 8, 3, 3, 4, 8, 9, 6, 3, 5, 9, 6, 10, 9, 7, 4, 11, 10, 10, 8, 13, 9, 5, 8, 8, 11, 7, 8, 10, 13, 11, 10, 12, 11, 13, 13, 16, 6, 16, 10, 21, 17

Offset: 0

Author

Stefano Spezia, Sep 01 2022

Keywords

• nonn
• base

Crossrefs

Cf. A047201, A055641, A356858.

Cf. A356860 (number of digits), A356861 (number of nonzero digits).

Programs

Mathematica

Table[Count[IntegerDigits[Product[Floor[(5i-1)/4], {i,n}]], 0], {n,0,80}]

Python

from math import prod
def a(n): return str(prod((5*k-1)//4 for k in range(1, n+1))).count("0")
print([a(n) for n in range(81)]) # Michael S. Branicky, Sep 01 2022

Formula

a(n) = A055641(A356858(n)).