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

%I A079099 #21 Jul 22 2025 14:25:11
%S A079099 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,
%T A079099 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,
%U A079099 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
%N A079099 Number of 0's in n primorial or 0's in A002110(n).
%C A079099 The sum of the reciprocals appear to converge.
%H A079099 Alois P. Heinz, <a href="/A079099/b079099.txt">Table of n, a(n) for n = 0..10000</a>
%p A079099 p:= proc(n) option remember; `if`(n<1, 1, p(n-1)*ithprime(n)) end:
%p A079099 a:= n-> nops([StringTools[SearchAll]("0", ""||(p(n)))]):
%p A079099 seq(a(n), n=0..90);  # _Alois P. Heinz_, Jul 21 2025
%t A079099 DigitCount[#,10,0]&/@FoldList[Times,Prime[Range[90]]] (* _Harvey P. Dale_, Mar 05 2022 *)
%o A079099 (PARI) a(n,dg=0) = { my(y=vecprod(primes(n))); #select(x->x==dg, digits(y)) }
%Y A079099 Cf. A002110, A067175.
%K A079099 nonn,base,easy
%O A079099 0,7
%A A079099 _Cino Hilliard_, Feb 03 2003
%E A079099 Offset corrected by _Alois P. Heinz_, Jul 21 2025