A079099 Number of 0's in n primorial or 0's in A002110(n).

0, 0, 0, 1, 1, 1, 3, 2, 1, 2, 1, 5, 2, 3, 4, 1, 3, 4, 3, 5, 4, 5, 4, 3, 5, 4, 8, 2, 3, 3, 6, 6, 7, 12, 12, 6, 6, 5, 9, 7, 8, 7, 7, 10, 9, 5, 9, 7, 9, 10, 17, 12, 11, 16, 16, 13, 10, 10, 14, 11, 14, 9, 16, 11, 14, 8, 13, 16, 14, 4, 15, 15, 17, 9, 19, 15, 17, 17, 22, 15, 12, 19, 14, 18, 11, 21, 19, 18, 19, 22, 15

Offset: 0

Author

Cino Hilliard, Feb 03 2003

Keywords

• nonn
• base
• easy

Comments

The sum of the reciprocals appear to converge.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A002110, A067175.

Programs

Maple

p:= proc(n) option remember; `if`(n<1, 1, p(n-1)*ithprime(n)) end:
a:= n-> nops([StringTools[SearchAll]("0", ""||(p(n)))]):
seq(a(n), n=0..90);  # Alois P. Heinz, Jul 21 2025

Mathematica

DigitCount[#,10,0]&/@FoldList[Times,Prime[Range[90]]] (* Harvey P. Dale, Mar 05 2022 *)

PARI

a(n,dg=0) = { my(y=vecprod(primes(n))); #select(x->x==dg, digits(y)) }

Extensions

Offset corrected by Alois P. Heinz, Jul 21 2025