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

0,1

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.

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

Example

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

Prog

(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

Crossrefs

Cf. A039986, A046810.

Sequence in context: A277469 A046888 A046890 * A046811 A046813 A208316

Adjacent sequences: A166918 A166919 A166920 * A166922 A166923 A166924

Keyword

nonn,base

Author

Pierre CAMI, Oct 23 2009

Extensions

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

Status

approved