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A069749 Number of primes less than 10^n containing only the digits 2 and 3 (A020458).

%I A069749 #16 May 23 2024 09:19:09
%S A069749 2,3,5,7,11,18,31,44,83,135,239,436,818,1436,2773,4695,9244,17022,
%T A069749 32948,58158,116040,214188,423902,791950,1554834,2904470,5725780,
%U A069749 10536383,21070698,40748211,79634658,148530950,296094802,561919901
%N A069749 Number of primes less than 10^n containing only the digits 2 and 3 (A020458).
%C A069749 a(22) / A006880(22) = 214188 / 201467286689315906290 =~ 10^-15. But out of the 2^22 candidates for primes, ~5% are.
%t A069749 s = 0; Do[k = 0; While[k < 2^n, k++; If[p = FromDigits[ PadLeft[ IntegerDigits[k, 2], n] + 2]; PrimeQ[p], s++ ]]; Print[s], {n, 1, 22}]
%t A069749 With[{c=Select[Flatten[Table[FromDigits/@Tuples[{2,3},n],{n,22}]], PrimeQ]}, Table[Count[c,_?(#<10^i&)],{i,22}]] (* _Harvey P. Dale_, Mar 18 2016 *)
%o A069749 (Python)
%o A069749 from sympy import isprime
%o A069749 from itertools import count, islice, product
%o A069749 def agen(): # generator of terms
%o A069749     c = 2
%o A069749     for d in count(2):
%o A069749         yield c
%o A069749         for first in product("23", repeat=d-1):
%o A069749             t = int("".join(first) + "3")
%o A069749             if isprime(t): c += 1
%o A069749 print(list(islice(agen(), 20))) # _Michael S. Branicky_, May 23 2024
%Y A069749 Cf. A006880, A020458 & A036937.
%K A069749 base,nonn,more
%O A069749 1,1
%A A069749 _Robert G. Wilson v_, Apr 22 2002
%E A069749 a(23)-a(27) from _Sean A. Irvine_, May 17 2024
%E A069749 a(28)-a(34) from _Michael S. Branicky_, May 22 2024