A254861 Number of primes less than 10^n that do not contain the string n.

0, 4, 22, 102, 903, 6310, 46706, 266823, 2774348, 16531372, 419285780, 3698719206, 33962823012

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Example

When n = 1, there are four primes less than 10: 2, 3, 5, and 7. None of these have 1 as a digit so a(1) = 4.

Mathematica

f[n_] := Block[{i}, Flatten@ Map[Length, Last@ Reap@ For[i = 0, i <= n, i++, Sow@ Select[Range[10^i], PrimeQ@ # && DigitCount[#][[i]] == 0 &]], {2}]]; f@ 7 (* Michael De Vlieger, Mar 26 2015 *)

Prog

(Sage) [len([p for p in prime_range(10^n) if not(str(n) in str(p))]) for n in [1..9]] # Tom Edgar, Feb 17 2015
(Python)
from sympy import primerange
def a(n):
    target = str(n)
    return sum(1 for p in primerange(1, 10**n) if target not in str(p))
print([a(n) for n in range(7)]) # Michael S. Branicky, Oct 30 2022

Crossrefs

Cf. A006880.

Sequence in context: A366759 A007901 A368289 * A088581 A017970 A220740

Adjacent sequences: A254858 A254859 A254860 * A254862 A254863 A254864

Keyword

nonn,base,more

Author

Asa Kaplan, Feb 09 2015

Extensions

a(7)-a(9) from Tom Edgar, Feb 17 2015

a(10) from Michael S. Branicky, Oct 30 2022

a(11) from Michael S. Branicky, Jun 01 2023

a(12) from Michael S. Branicky, Jul 06 2023

Status

approved