A053095 Number of primes having exactly the same digits as appear in first n primes.

1, 1, 1, 8, 62, 568, 5370, 114546, 2898058, 0, 1119268465, 26053674813

Offset: 1

Author

Enoch Haga, Mar 19 2000

Keywords

• base
• nonn
• more

Comments

a(n) = 0 if sum of digits is a multiple of three (see A103208). - Ray Chandler, Apr 07 2010

Examples

			a(4) = 8 because the first four prime n, concatenated, are 2+3+5+7 or 2357. There are 8 prime arrangements: 2357, 2753, 3257, 3527, 5237, 5273, 7253, 7523.
		

Crossrefs

Cf. A054260, A053160, A053161, A103208.

Programs

Python

from sympy import isprime, prime
from sympy.utilities.iterables import multiset_permutations
def A053095(n):
    return sum(1 for d in multiset_permutations(''.join(str(prime(m+1)) for m in range(n))) if isprime(int(''.join(d)))) # Chai Wah Wu, Mar 17 2019

Extensions

a(7)-a(9) from Ray Chandler, Apr 07 2010

a(10) from Ray Chandler, Apr 08 2010

a(11) from Michael S. Branicky, Mar 17 2025

a(12) from Michael S. Branicky, Apr 07 2025