A091709 Number of primes less than 10^n having at least one digit 8.

0, 2, 27, 314, 3217, 31699, 308774, 2987107, 28824402, 277779084, 2674980022, 25752370493, 247919235555, 2387154761520

Offset: 1

Author

Enoch Haga, Jan 30 2004

Keywords

• nonn
• base
• more

Examples

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

Crossrefs

a(n) + A091642(n) = A006880(n).

Cf. A091644, A091645, A091646, A091647, A090705, A090706, A091707, A091708, 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], 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' 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

Extensions

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

3 more terms from Ryan Propper, Aug 22 2005

a(13) from Robert Price, Nov 11 2013

a(14) from Giovanni Resta, Jul 21 2015