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A091643
Number of primes less than 10^n which do not contain the digit 9.
30
4, 19, 108, 687, 4766, 35139, 267486, 2083814, 16531372, 133059504, 1082995490, 8896945667, 73651718719, 613664827254
OFFSET
1,1
FORMULA
Number of primes less than 10^n after removing any primes with at least one digit 9.
a(n) = A006880(n) - A091710(n).
a(n) <= max(4,24*(9^(n-2))) <= 1 + (9^n)/3 (see formula in A091634). - Chai Wah Wu, Sep 17 2018
EXAMPLE
a(2) = 19 because of the 25 primes less than 10^2, 6 have at least one digit 9; 25-6 = 19.
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], 9] == {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* Robert G. Wilson v, Feb 02 2004 *)
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