A119291 Total number of zero digits in first 10^n primes.

0, 9, 191, 3303, 46188, 557005, 6481183, 76292782, 881025347, 9763247930, 106864564286, 1162019145892

Offset: 1

Author

Enoch Haga, May 13 2006

Keywords

• more
• nonn
• base

Comments

Count the zero digits in the first 10^n primes.

Examples

			a(2)=9 since there are 9 zero digits in the first 100 primes.
		

Crossrefs

Cf. A119290, A119292-A119300.

Programs

Maple

A055641 := proc(n) local a,d ; a := 0 ; for d in convert(n,base,10) do if d = 0 then a := a+1 ; fi ; od: a ; end: p := 2: n := 1: c :=0 : nsw := 10 : while true do n := n+1 ; p := nextprime(p) ; c := c+A055641(p) ; if n = nsw then print(c) ; nsw := 10*nsw ; fi ; od: # R. J. Mathar, May 30 2008

Mathematica

Table[Count[IntegerDigits[Prime[Range[10^n]]], 0, 2], {n, 6}] (* Robert Price, May 02 2019 *)

PARI

my(x=10, i=0, j=0); forprime(p=1, , j++; my(d=digits(p)); i+=#setintersect(vecsort(d), vector(#d, t, 0)); if(j==x, print1(i, ", "); x=10*x)) \\ Felix Fröhlich, May 02 2019

Formula

a(n) = Sum_{j=1..10^n} A055641(A000040(j)). - R. J. Mathar, May 30 2008

Extensions

a(8)-a(11) from Robert Price, Nov 05 2013

a(12) from Marek Hubal, Mar 04 2019