A369877 - OEIS

%I #67 Mar 23 2024 08:24:47

%S 263,1933,3319,3391,3931,9133,11393,11933,12163,12241,12421,12613,

%T 13913,13931,14221,16231,21163,21613,24121,26113,31139,31193,31319,

%U 31391,32611,33119,33191,33911,39113,41221,61231,62131,62311,63211,91331,93113,93131,111263

%N 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.

%C 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

%H Michael S. Branicky, <a href="/A369877/b369877.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

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

%o (Python)

%o from math import prod

%o from sympy import isprime

%o def ok(n):

%o     if not isprime(n): return False

%o     s = str(n)

%o     p, np = [d for d in s if d in "2357"], [d for d in s if d in "014689"]

%o     return p and prod(map(int, p)) == prod(map(int, np))

%o print([k for k in range(10**5) if ok(k)]) # _Michael S. Branicky_, Mar 22 2024

%Y Cf. A000040, A156343.

%K nonn,base

%O 1,1

%A _Gonzalo Martínez_, Mar 19 2024