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%I #26 Mar 17 2021 02:52:09
%S 3,16,102,668,4715,34813,265015,2067152,16413535,132200223,1076692515,
%T 8849480283,73288053795,610860050965
%N Number of primes less than 10^n which do not contain the digit 3.
%C Number of primes less than 10^n after removing any primes with at least one digit 3.
%F a(n) = A006880(n) - A091647(n).
%e a(2)=16 because there are 25 primes less than 10^2, 9 have at least one digit 3; 25-9 = 16.
%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], 3] == {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* _Robert G. Wilson v_, Feb 02 2004 *)
%t Table[Count[Prime[Range[PrimePi[10^n]]],_?(DigitCount[#,10,3]==0&)],{n,8}] (* _Harvey P. Dale_, Oct 04 2011 *)
%o (PARI) good(n)=n=eval(Vec(Str(n)));for(i=1,#n,if(n[i]==3,return(1)));0
%o a(n)=my(s);forprime(p=2,10^n,s+=good(p));s \\ _Charles R Greathouse IV_, Oct 04 2011
%o (Python)
%o from sympy import primerange
%o def a(n): return sum('3' not in str(p) for p in primerange(2, 10**n))
%o print([a(n) for n in range(1, 7)]) # _Michael S. Branicky_, Mar 16 2021
%Y Cf. A091634, A091635, A091636, A091638, A091639, A091640, A091641, A091642, A091643.
%K 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
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