A091641 Number of primes less than 10^n which do not contain the digit 7.

3, 16, 100, 680, 4773, 34992, 266823, 2079512, 16503238, 132852644, 1081509855, 8885472675, 73563855306, 612982476612

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 7.

Examples

			a(2) = 16 because of the 25 primes less than 10^2, 9 have at least one digit 7; 25-9=16.
		

Crossrefs

Cf. A091634, A091635, A091636, A091637, A091638, A091639, A091640, A091642, 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], 7] == {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* Robert G. Wilson v, Feb 02 2004 *)

Python

from sympy import primerange
def a(n): return sum('7' not in str(p) for p in primerange(2, 10**n))
print([a(n) for n in range(1, 7)]) # Michael S. Branicky, Mar 16 2021

Formula

a(n) = A006880(n) - A091708(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