A140532 Number of primes with n distinct decimal digits, none of which are 0.

4, 20, 83, 395, 1610, 5045, 12850, 23082, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Norman Morton (mathtutorer(AT)yahoo.com), Jul 03 2008

Keywords

• nonn
• base

Comments

a(9) is zero because 1+2+...+9 = 45 which is divisible by 3, making any number with 9 distinct digits also divisible by 3. - Wei Zhou, Oct 02 2011

The maximal distinct-digit prime without 0's is 98765431. Thus, a(n) = 0 for n >= 9. - Michael S. Branicky, Apr 20 2021

Examples

			a(1) = #{2,3,5,7} = 4.
a(2) = #{13,17,19,23,...,97} = 20. Note that the prime 11 is omitted because its decimal digits are not distinct.
		

Crossrefs

Cf. A112371, A073532.

Programs

Mathematica

Length /@ Table[Select[FromDigits /@ Permutations[Range@9, {i}], PrimeQ], {i,9}] (* Wei Zhou, Oct 02 2011 *)

Python

from itertools import permutations
from sympy import isprime, primerange
def distinct_digs(n): s = str(n); return len(s) == len(set(s))
def a(n):
  if n >= 9: return 0
  return sum(isprime(int("".join(p))) for p in permutations("123456789", n))
print([a(n) for n in range(1, 30)]) # Michael S. Branicky, Apr 20 2021

Extensions

Corrected by Charles R Greathouse IV, Aug 02 2010