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Number of 0's in n primorial or 0's in A002110(n).
1

%I #5 Mar 05 2022 11:19:54

%S 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 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 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

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

%C The sum of the reciprocals appear to converge.

%t DigitCount[#,10,0]&/@FoldList[Times,Prime[Range[90]]] (* _Harvey P. Dale_, Mar 05 2022 *)

%o (PARI) \ prime factorials p# = p1*p2*p3... where pi is the ithprime prfactdg(n,dg) = { forprime(j=2,n, y=1; ct=sr=0; forprime(x=2,j, y*=x; ); y1 = Str(y); print1(y" "); ln = length(y1); for(k = 1,ln, d = y%10; y = floor(y/10); if(d ==dg, ct+=1; sr += 1.0/ct; ); ); print1(ct","); ); print(); print(sr); }

%K easy,nonn

%O 2,6

%A _Cino Hilliard_, Feb 03 2003