A087527 Primes consisting only of digits 2 and 3 occurring with equal frequency.

23, 23223323, 32323223, 2222323333, 2223223333, 2232223333, 2232322333, 2232332233, 2323222333, 2332322233, 2333222323, 2333223223, 3223232323, 3232222333, 3232232233, 3232233223, 3232322323, 3323232223, 22222232333333, 22222322333333, 22222323233333

Offset: 1

Author

Paul D. Hanna and Amarnath Murthy, Sep 12 2003

Keywords

• base
• nonn

Comments

There are 18 digit pairs which can produce such primes. (1,0),(1,3),(1,4),(1,6),(1,7),(1,9),(2,3),(2,9),(3,4),(3,5),(3,7),(3,8),(4,7),(4,9),(5,9),(6,7),(7,9),(8,9).

Links

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

Crossrefs

Cf. A087510, A087511, A087515.

Programs

PARI

\\ Needs B() from A087510.
concat(vector(6,k,B(k,2,3,isprime))) \\ Andrew Howroyd, Sep 21 2024

Python

from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def auptodigs(maxdigits):
    alst = []
    for d in range(2, maxdigits + 1, 2):
        ms = "2"*(d//2) + "3"*(d//2 - 1)
        for p in multiset_permutations(ms, d-1):
            t = int("".join(p) + "3")
            if isprime(t):
                alst.append(t)
    return alst
print(auptodigs(10)) # Michael S. Branicky, Jan 11 2022

Extensions

Offset changed to 1 and a(19) corrected by Georg Fischer, Jan 11 2022