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Number of primes less than 10^n which do not contain the digit 4.
10

%I #13 Mar 20 2017 04:39:11

%S 4,22,136,903,6361,46545,354123,2761106,21925170,176544507,1437663500,

%T 11814853749,97837428598,815398741896

%N Number of primes less than 10^n which do not contain the digit 4.

%F Number of primes less than 10^n after removing any primes with at least one digit 4.

%F a(n) = A006880(n) - A091705(n).

%e a(2) = 22 because of the 25 primes less than 10^2, 3 have at least one digit 4; 25-3 = 22.

%t 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], 4] == {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* _Robert G. Wilson v_, Feb 02 2004 *)

%Y Cf. A091634, A091635, A091636, A091637, A091639, A091640, A091641, A091642, A091643.

%K more,nonn,base

%O 1,1

%A _Enoch Haga_, Jan 30 2004

%E Edited and extended by _Robert G. Wilson v_, Feb 02 2004

%E a(9)-a(12) from _Donovan Johnson_, Feb 14 2008

%E a(13) from _Robert Price_, Nov 08 2013

%E a(14) from _Giovanni Resta_, Mar 20 2017