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

0,7

Comments

The sum of the reciprocals appear to converge.

Links

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

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 *)

Prog

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

Crossrefs

Cf. A002110, A067175.

Sequence in context: A254629 A096248 A079109 * A213195 A256794 A366899

Adjacent sequences: A079096 A079097 A079098 * A079100 A079101 A079102

Keyword

nonn,base,easy

Author

Cino Hilliard, Feb 03 2003

Extensions

Offset corrected by Alois P. Heinz, Jul 21 2025

Status

approved