A046890 a(n) is the least integer that has exactly n anagrams that are primes.

1, 2, 13, 113, 149, 1013, 1039, 1247, 1123, 1349, 1579, 1237, 10127, 10238, 10139, 10235, 10234, 10457, 11579, 10789, 10237, 11239, 12457, 10279, 12349, 12347, 13678, 12359, 14579, 13489, 10379, 12367, 12389, 23579, 13579, 100349, 12379

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• base

Comments

An anagram is a permutation of digits not beginning with 0.

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..8004 (search of numbers with <= 12 digits; terms 0..511 from Chai Wah Wu)

Crossrefs

Cf. A046810.

Programs

Mathematica

ap[n_] := Count[FromDigits /@ Select[Permutations[IntegerDigits[n]], First[#] != 0 &], ?PrimeQ]; t = {1}; Do[i = 1; While[ap[i] != n, i++]; AppendTo[t, i], {n, 30}]; t (* _Jayanta Basu, Jun 29 2013 *)

Python

from sympy import isprime
from sympy.utilities.iterables import multiset_permutations as mp
from itertools import count, islice, combinations_with_replacement as mc
def nd(d): yield from ("".join((f,)+m) for f in "123456789" for m in mc("0123456789", d-1))
def c(s): return sum(1 for p in mp(s) if p[0]!="0" and isprime(int("".join(p))))
def agen(): # generator of sequence terms
    n, adict = 0, dict()
    for digs in count(1):
        for s in nd(digs):
            v = c(s)
            if v not in adict: adict[v] = int(s)
            while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 40))) # Michael S. Branicky, Feb 08 2023