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A091634 Number of primes less than 10^n which do not contain the digit 0.

%I A091634 #35 Aug 27 2021 18:23:24
%S A091634 4,25,153,1010,7122,52313,397866,3103348,24649318,198536215,
%T A091634 1616808581,13287264748,110033428309,917072930187
%N A091634 Number of primes less than 10^n which do not contain the digit 0.
%F A091634 Number of primes less than 10^n after removing any primes with at least one digit 0.
%F A091634 a(n) <= A052386(n) = 9*(9^n-1)/8. - _Charles R Greathouse IV_, Sep 13 2016
%F A091634 a(n) <= (9^n-1)/2 = A052386(n)*4/9 since the last digit of a prime of n digits can only be one of 4 numbers, (2,3,5,7) when n = 1 and (1,3,7,9) when n > 1. - _Chai Wah Wu_, Mar 18 2018
%e A091634 a(3) = 153 because there are 168 primes less than 10^3, 15 primes have at least one zero; 168 - 15 = 153.
%t A091634 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], 0] == {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* _Robert G. Wilson v_, Feb 02 2004 *)
%t A091634 Table[PrimePi[10^n]-Total[Boole[DigitCount[#,10,0]>0]&/@ Prime[ Range[ PrimePi[ 10^n]]]],{n,8}] (* The program generates the first 8 terms of the sequence. To generate more, increase the digit 8 but the program may take a long time to run. *) (* _Harvey P. Dale_, Aug 26 2021 *)
%o A091634 (Python)
%o A091634 from sympy import sieve # use primerange for larger terms
%o A091634 def nodigs0(n): return '0' not in str(n)
%o A091634 def aupton(terms):
%o A091634   ps, alst = 0, []
%o A091634   for n in range(1, terms+1):
%o A091634     ps += sum(nodigs0(p) for p in sieve.primerange(10**(n-1), 10**n))
%o A091634     alst.append(ps)
%o A091634   return alst
%o A091634 print(aupton(7)) # _Michael S. Branicky_, Apr 25 2021
%Y A091634 a(n) + A091644(n) = A006880(n).
%Y A091634 Cf. A091635, A091636, A091637, A091638, A091639, A091640, A091641, A091642, A091643.
%K A091634 nonn,base,more
%O A091634 1,1
%A A091634 _Enoch Haga_, Jan 30 2004
%E A091634 Edited and extended by _Robert G. Wilson v_, Feb 02 2004
%E A091634 a(9)-a(12) from _Donovan Johnson_, Feb 14 2008
%E A091634 a(13) from _Robert Price_, Nov 08 2013
%E A091634 a(14) from _Giovanni Resta_, Mar 20 2017