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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.
1
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
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
Sequence in context: A343192 A023314 A054802 * A239685 A108823 A229480
KEYWORD
nonn,base
AUTHOR
Gonzalo Martínez, Mar 19 2024
STATUS
approved