A091642 Number of primes less than 10^n which do not contain the digit 8.

4, 23, 141, 915, 6375, 46799, 355805, 2774348, 22023132, 177273427, 1443074791, 11855541525, 98146301284, 817786989282

Offset: 1

Author

Enoch Haga, Jan 30 2004

Keywords

• more
• nonn
• base

Examples

			a(2) = 23 because of the 25 primes less than 10^2, 2 have at least one digit 8; 25-2 = 23.
		

Crossrefs

Cf. A091634, A091635, A091636, A091637, A091638, A091639, A091640, A091641, A091643.

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], 8] == {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* Robert G. Wilson v, Feb 02 2004 *)

Python

from sympy import sieve # use slower primerange for larger terms
def a(n): return sum('8' not in str(p) for p in sieve.primerange(2, 10**n))
print([a(n) for n in range(1, 8)]) # Michael S. Branicky, Apr 23 2021

Formula

Number of primes less than 10^n after removing any primes with at least one digit 8.

a(n) = A006880(n) - A091709(n).

Extensions

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

a(9)-a(12) from Donovan Johnson, Feb 14 2008

a(13) from Robert Price, Nov 08 2013

a(14) from Giovanni Resta, Mar 20 2017