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A091642
Number of primes less than 10^n which do not contain the digit 8.
10
4, 23, 141, 915, 6375, 46799, 355805, 2774348, 22023132, 177273427, 1443074791, 11855541525, 98146301284, 817786989282
OFFSET
1,1
FORMULA
Number of primes less than 10^n after removing any primes with at least one digit 8.
a(n) = A006880(n) - A091709(n).
EXAMPLE
a(2) = 23 because of the 25 primes less than 10^2, 2 have at least one digit 8; 25-2 = 23.
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 *)
PROG
(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
KEYWORD
more,nonn,base
AUTHOR
Enoch Haga, Jan 30 2004
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
STATUS
approved