A091635 Number of primes less than 10^n which do not contain the digit 1.

4, 17, 101, 670, 4675, 34425, 262549, 2051466, 16312743, 131464721, 1071368863, 8809580516, 72986908554, 608542410004

Offset

1,1

Links

Table of n, a(n) for n=1..14.

Formula

Number of primes less than 10^n after removing any primes with at least one digit 1.

a(n) = A006880(n) - A091645(n).

Example

a(2) = 17 because of the 25 primes less than 10^2, 8 have at least one digit 1; 25-8 = 17.

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

Prog

(Python)
from sympy import sieve # import/use primerange for larger terms
def a(n): return sum('1' not in str(p) for p in sieve.primerange(1, 10**n))
print([a(n) for n in range(1, 8)]) # Michael S. Branicky, Apr 17 2021

Crossrefs

Cf. A091634, A091636, A091637, A091638, A091639, A091640, A091641, A091642, A091643.

Sequence in context: A024052 A128321 A290352 * A306160 A127676 A335626

Adjacent sequences: A091632 A091633 A091634 * A091636 A091637 A091638

Keyword

nonn,base,more

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