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Number of primes less than 10^n having at least one digit 6.
10

%I #18 Apr 23 2021 11:57:07

%S 0,2,32,332,3225,31792,309431,2991216,28863327,278085918,2677289604,

%T 25769815303,248050788931,2388172543971

%N Number of primes less than 10^n having at least one digit 6.

%e a(1) = 0 because of the 4 primes less than 10^1, none have at least one digit 6.

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

%o (Python)

%o from sympy import sieve # use slower primerange for larger terms

%o def a(n): return sum('6' in str(p) for p in sieve.primerange(2, 10**n))

%o print([a(n) for n in range(1, 8)]) # _Michael S. Branicky_, Apr 23 2021

%Y a(n) + A091640(n) = A006880(n).

%Y Cf. A091644, A091645, A091646, A091647, A091705, A091706, A091708, A091709, A091710.

%K nonn,base

%O 1,2

%A _Enoch Haga_, Jan 30 2004

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

%E 3 more terms from _Ryan Propper_, Aug 21 2005

%E a(13) from _Robert Price_, Nov 11 2013

%E a(14) from _Giovanni Resta_, Jul 21 2015