A091639 Number of primes less than 10^n which do not contain the digit 5.

3, 22, 136, 905, 6310, 46549, 354910, 2765749, 21955845, 176781643, 1439380189, 11827571824, 97933795005, 816144146010

Offset: 1

Author

Enoch Haga, Jan 30 2004

Keywords

• more
• nonn
• base

Comments

Number of primes less than 10^n after removing any primes with at least one digit 5.

Examples

			a(2) = 22 because of the 25 primes less than 10^2, 3 have at least one digit 5; 25-3 = 22.
		

Crossrefs

Cf. A091634, A091635, A091636, A091637, A091638, A091640, A091641, A091642, A091643.

Cf. A006880, A091706.

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

Python

from sympy import primerange
def a(n): return sum('5' not in str(p) for p in primerange(2, 10**n))
print([a(n) for n in range(1, 7)]) # Michael S. Branicky, Mar 22 2021

Formula

a(n) = A006880(n) - A091706(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