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A091644 Number of primes less than 10^n which have at least one digit 0. 9
0, 0, 15, 219, 2470, 26185, 266713, 2658107, 26198216, 256516296, 2501246232, 24320647270, 236032108530, 2287868820615 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
3 additional terms, generated using a sieve program. - Ryan Propper, Aug 20 2005
LINKS
FORMULA
a(n) = A006880(n) - A091634(n).
EXAMPLE
a(3) = 15 because of the 168 primes less than 10^3, 15 have at least one 0 digit.
MATHEMATICA
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 *)
PROG
(Python)
from sympy import sieve # use primerange for larger terms
def digs0(n): return '0' in str(n)
def aupton(terms):
ps, alst = 0, []
for n in range(1, terms+1):
ps += sum(digs0(p) for p in sieve.primerange(10**(n-1), 10**n))
alst.append(ps)
return alst
print(aupton(7)) # Michael S. Branicky, Apr 25 2021
CROSSREFS
Sequence in context: A081196 A020287 A152272 * A238538 A289160 A027843
KEYWORD
nonn,base,more
AUTHOR
Enoch Haga, Jan 30 2004
EXTENSIONS
Edited and extended by Robert G. Wilson v, Feb 02 2004
More terms from Ryan Propper, Aug 20 2005
a(13) from Robert Price, Nov 11 2013
a(14) from Giovanni Resta, Jul 21 2015
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)