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

1,1

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000040, A156343.

Sequence in context: A343192 A023314 A054802 * A239685 A108823 A229480

Adjacent sequences: A369874 A369875 A369876 * A369878 A369879 A369880

Keyword

nonn,base

Author

Gonzalo Martínez, Mar 19 2024

Status

approved