A156343 -id:A156343 - cp's OEIS frontend

A371352 Prime numbers such that the sum of their prime digits is equal to the sum of their nonprime digits.

167, 211, 541, 617, 761, 853, 1021, 1201, 1423, 1559, 1607, 1973, 2011, 2143, 2341, 2383, 2833, 3467, 3719, 3823, 3917, 4051, 4231, 4637, 4673, 5261, 5443, 5519, 5591, 6473, 6521, 6701, 7193, 7643, 7687, 7867, 8053, 8233, 8677, 9137, 9173, 9371, 9551

Offset: 1

Gonzalo Martínez, Mar 19 2024

			9173 is a term because it is a prime number whose prime digits and nonprime digits have the same sum: 3 + 7 = 1 + 9 = 10.

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

Cf. A000040, A156343 (equal number of prime and nonprime digits).

Select[Prime[Range[1200]], Plus @@ Select[d = IntegerDigits[#], PrimeQ[#1] &] == Plus @@ Select[d, ! PrimeQ[#1] &] &] (* Amiram Eldar, Mar 22 2024 *)

from sympy import isprime
def ok(n):
    if not isprime(n): return False
    s, sums = str(n), [0, 0]
    for c in s: sums[int(c in "2357")] += int(c)
    return sums[0] == sums[1]
print([k for k in range(10**4) if ok(k)]) # Michael S. Branicky, Apr 23 2024

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.

Original entry on oeis.org

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

Gonzalo Martínez, Mar 19 2024

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

			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.

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

Cf. A000040, A156343.

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

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

cp's OEIS Frontend

A371352 Prime numbers such that the sum of their prime digits is equal to the sum of their nonprime digits.

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