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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.

%I A369877 #67 Mar 23 2024 08:24:47
%S A369877 263,1933,3319,3391,3931,9133,11393,11933,12163,12241,12421,12613,
%T A369877 13913,13931,14221,16231,21163,21613,24121,26113,31139,31193,31319,
%U A369877 31391,32611,33119,33191,33911,39113,41221,61231,62131,62311,63211,91331,93113,93131,111263
%N 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.
%C A369877 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 A369877 Michael S. Branicky, <a href="/A369877/b369877.txt">Table of n, a(n) for n = 1..10000</a>
%e A369877 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 A369877 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 A369877 (Python)
%o A369877 from math import prod
%o A369877 from sympy import isprime
%o A369877 def ok(n):
%o A369877     if not isprime(n): return False
%o A369877     s = str(n)
%o A369877     p, np = [d for d in s if d in "2357"], [d for d in s if d in "014689"]
%o A369877     return p and prod(map(int, p)) == prod(map(int, np))
%o A369877 print([k for k in range(10**5) if ok(k)]) # _Michael S. Branicky_, Mar 22 2024
%Y A369877 Cf. A000040, A156343.
%K A369877 nonn,base
%O A369877 1,1
%A A369877 _Gonzalo Martínez_, Mar 19 2024