

A166921


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


2



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
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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



