A228421 Count of the first 10^n primes which do not contain the digit 9.

1, 8, 69, 620, 5010, 45732, 418142, 3785060, 32579606, 296601070, 2683254222, 24354108057, 212324183352

Offset: 0

Author

Robert Price, Nov 09 2013

Keywords

• more
• nonn
• base
• hard

Examples

			a(1) = 8 since there are 8 primes in the first 10 (through 29) that do not contain a 9.  Namely: 2, 3, 5, 7, 11, 13, 17, 23.
		

Crossrefs

Cf. A231412, A228413-A228421, A097952, A091634-A091643.

Programs

Mathematica

Table[Length[Select[Range[10^n], DigitCount[Prime[#], 10, 9] == 0 &]], {n, 0, 5}] (* Robert Price, Mar 23 2020 *)

Python

def a(n):
    count = 0
    for k in range(1,10**n+1):
        if '9' not in str(prime(k)):
            count += 1
    return count
n = 0
while n < 10:
    print(a(n), end=', ')
    n += 1
# Derek Orr, Jul 27 2014

Formula

a(n) <= 9^n. - Charles R Greathouse IV, May 21 2014

Extensions

a(12) from Lucas A. Brown, Mar 19 2024