A046891 Values of n where number of permutations of digits a(n) that are prime increases.

1, 2, 13, 103, 107, 1007, 1013, 1049, 1079, 1237, 10013, 10039, 10079, 10139, 10237, 10279, 10379, 13789, 100127, 100139, 100235, 100237, 100279, 101237, 101239, 102347, 102367, 102379, 103579, 103789, 1001234, 1001237, 1001239, 1002347, 1002359, 1002367, 1002379

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..91

Crossrefs

Cf. A039999, A046892.

Programs

Mathematica

ap[n_] := Count[FromDigits /@ Permutations[IntegerDigits[n]], ?PrimeQ]; t = {1}; x = 0; Do[If[ap[i] > x, AppendTo[t, i]; x = ap[i]], {i, 105000}]; t (* _Jayanta Basu, Jun 29 2013 *)

Python

from sympy import prime
from gmpy2 import is_prime
from sympy.utilities.iterables import multiset_permutations as mp
from itertools import count, islice, combinations_with_replacement as mc
def f(n): return sum(1 for p in mp(str(n)) if is_prime(t:=int("".join(p))))
def bgen(d):
    for f in "123456789":
        yield from map(int, (f+"".join(m) for m in mc("0123456789", d-1)))
def agen():
    record = -1
    for d in count(1):
        for k in bgen(d):
            v = f(k)
            if v > record:
                record = v
                yield k
print(list(islice(agen(), 30))) # Michael S. Branicky, Feb 17 2024

Extensions

a(35) and beyond from Michael S. Branicky, Feb 17 2024