A091644 Number of primes less than 10^n which have at least one digit 0.

0, 0, 15, 219, 2470, 26185, 266713, 2658107, 26198216, 256516296, 2501246232, 24320647270, 236032108530, 2287868820615

Offset: 1

Author

Enoch Haga, Jan 30 2004

Keywords

• nonn
• base
• more

Comments

3 additional terms, generated using a sieve program. - Ryan Propper, Aug 20 2005

Examples

			a(3) = 15 because of the 168 primes less than 10^3, 15 have at least one 0 digit.
		

Crossrefs

Cf. A091645, A091646, A091647, A091705, A091706, A091707, A091708, A091709, A091710.

Programs

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ ! PrimeQ[k], k++ ]; k]; c = 0; p = 1; Do[ While[ p = NextPrim[p]; p < 10^n, If[ Position[ IntegerDigits[p], 0] != {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* Robert G. Wilson v, Feb 02 2004 *)

Python

from sympy import sieve # use primerange for larger terms
def digs0(n): return '0' in str(n)
def aupton(terms):
  ps, alst = 0, []
  for n in range(1, terms+1):
    ps += sum(digs0(p) for p in sieve.primerange(10**(n-1), 10**n))
    alst.append(ps)
  return alst
print(aupton(7)) # Michael S. Branicky, Apr 25 2021

Formula

a(n) = A006880(n) - A091634(n).

Extensions

Edited and extended by Robert G. Wilson v, Feb 02 2004

More terms from Ryan Propper, Aug 20 2005

a(13) from Robert Price, Nov 11 2013

a(14) from Giovanni Resta, Jul 21 2015