A369877 Prime numbers p such that the product of their prime digits is equal to the product of their nonprime digits, where p has at least one prime digit.

263, 1933, 3319, 3391, 3931, 9133, 11393, 11933, 12163, 12241, 12421, 12613, 13913, 13931, 14221, 16231, 21163, 21613, 24121, 26113, 31139, 31193, 31319, 31391, 32611, 33119, 33191, 33911, 39113, 41221, 61231, 62131, 62311, 63211, 91331, 93113, 93131, 111263

Offset: 1

Author

Gonzalo Martínez, Mar 19 2024

Keywords

• nonn
• base

Comments

Terms must contain at least one prime digit (else 11 would be a term); no term contains a decimal digit 0, 5, or 7. - Michael S. Branicky, Mar 22 2024

Examples

			12163 is a term because it is a prime number whose prime digits and nonprime digits have the same product: 2 * 3 = 1 * 1 * 6.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A156343.

Programs

Mathematica

Select[Prime[Range[11500]], Length[dp = Select[d = IntegerDigits[#], PrimeQ[#1] &]] > 0 && Times @@ dp == Times @@ Select[d, !PrimeQ[#1] &] &] (* Amiram Eldar, Mar 22 2024 *)

Python

from math import prod
from sympy import isprime
def ok(n):
    if not isprime(n): return False
    s = str(n)
    p, np = [d for d in s if d in "2357"], [d for d in s if d in "014689"]
    return p and prod(map(int, p)) == prod(map(int, np))
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Mar 22 2024