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

0,7

Links

Table of n, a(n) for n=0..80.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A047201, A055641, A356858.

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

Sequence in context: A294019 A123721 A077618 * A085863 A220354 A344478

Adjacent sequences: A356856 A356857 A356858 * A356860 A356861 A356862

Keyword

nonn,base

Author

Stefano Spezia, Sep 01 2022

Status

approved