A091640 - OEIS

A091640

Number of primes less than 10^n which do not contain the digit 6.

4, 23, 136, 897, 6367, 46706, 355148, 2770239, 21984207, 176966593, 1440765209, 11838096715, 98014747908, 816769206831

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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 6.

a(n) = A006880(n) - A091707(n).

EXAMPLE

a(2) = 23 because of the 25 primes less than 10^2, 2 have at least one digit 6; 25-2 = 23.

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

PROG

(Python)

from sympy import sieve # use slower primerange for larger terms

def a(n): return sum('6' not 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

CROSSREFS

Cf. A091634, A091635, A091636, A091637, A091638, A091639, A091641, A091642, A091643.

Sequence in context: A193808 A038723 A302761 * A237362 A067110 A290052

Adjacent sequences: A091637 A091638 A091639 * A091641 A091642 A091643

KEYWORD

more,nonn,base

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