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

Offset

1,1

Comments

There are 18 digit pairs which can produce such primes. (1,0),(7,0),(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).

Links

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

Prog

(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
(PARI) seq(n, d1=2, d2=3)={my(L=List()); for(d=1, oo, forperm(vector(2*d, i, if(i<=d, d1, d2)), v, my(q=fromdigits(Vec(v))); if(isprime(q), listput(L, q); if(#L>=n, return(Vec(L)) ) )))} \\ Andrew Howroyd, Jan 11 2022

Crossrefs

Cf. A087510, A087511, A087514.

Sequence in context: A124993 A013818 A290118 * A013906 A214360 A030464

Adjacent sequences: A087524 A087525 A087526 * A087528 A087529 A087530

Keyword

base,nonn

Author

Paul D. Hanna and Amarnath Murthy, Sep 12 2003

Extensions

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

Status

approved