|
%I #22 Apr 25 2021 12:19:22
%S 0,0,15,219,2470,26185,266713,2658107,26198216,256516296,2501246232,
%T 24320647270,236032108530,2287868820615
%N Number of primes less than 10^n which have at least one digit 0.
%C 3 additional terms, generated using a sieve program. - _Ryan Propper_, Aug 20 2005
%F a(n) = A006880(n) - A091634(n).
%e a(3) = 15 because of the 168 primes less than 10^3, 15 have at least one 0 digit.
%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], 0] != {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* _Robert G. Wilson v_, Feb 02 2004 *)
%o (Python)
%o from sympy import sieve # use primerange for larger terms
%o def digs0(n): return '0' in str(n)
%o def aupton(terms):
%o ps, alst = 0, []
%o for n in range(1, terms+1):
%o ps += sum(digs0(p) for p in sieve.primerange(10**(n-1), 10**n))
%o alst.append(ps)
%o return alst
%o print(aupton(7)) # _Michael S. Branicky_, Apr 25 2021
%Y Cf. A091645, A091646, A091647, A091705, A091706, A091707, A091708, A091709, A091710.
%K nonn,base,more
%O 1,3
%A _Enoch Haga_, Jan 30 2004
%E Edited and extended by _Robert G. Wilson v_, Feb 02 2004
%E More terms from _Ryan Propper_, Aug 20 2005
%E a(13) from _Robert Price_, Nov 11 2013
%E a(14) from _Giovanni Resta_, Jul 21 2015
|
