A166921 Least prime with exactly n prime anagrams not equal to itself.

2, 13, 113, 149, 1013, 1039, 1427, 1123, 1439, 1579, 1237, 10271, 10453, 10139, 10253, 10243, 10457, 11579, 10789, 10273, 11239, 12457, 10729, 13249, 12347, 13687, 12539, 14759, 13799, 10739, 12637, 12893, 23957, 13597, 100493, 12379, 14593, 101383, 13789

Offset: 0

Author

Pierre CAMI, Oct 23 2009

Keywords

• nonn
• base

Comments

13 has only one prime anagram (31), and no smaller prime has a prime anagram other than itself, so a(1) = 13.

113 has 2 prime anagrams (131 and 311), and no smaller prime has two prime anagrams other than itself, so a(2) = 113.

149 has 3 prime anagrams (419, 491, and 941), and no smaller prime has three prime anagrams other than itself, so a(3) = 149.

Examples

			a(7) = prime 1123 with 7 prime anagrams 1213, 1231, 1321, 2113, 2131, 2311, 3121.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..2780 (terms 83..223 from P. CAMI and Chai Wah Wu, and terms 1..82 from P. CAMI)
• Michael S. Branicky, Python program

Crossrefs

Cf. A039986, A046810.

Programs

Python

# see link for faster version
from sympy import isprime
from itertools import permutations
def anagrams(n):
  s = str(n)
  return set(int("".join(p)) for p in permutations(s) if p[0] != '0')
def num_prime_anagrams(n): return sum(isprime(i) for i in anagrams(n))
def a(n):
  if n == 0: return 2
  k = 3
  while not isprime(k) or num_prime_anagrams(k) != n+1: k += 2
  return k
print([a(n) for n in range(39)]) # Michael S. Branicky, Feb 13 2021

Extensions

Definition edited and a(0) added by Chai Wah Wu, Dec 26 2016