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A087527
Primes consisting only of digits 2 and 3 occurring with equal frequency.
4
23, 23223323, 32323223, 2222323333, 2223223333, 2232223333, 2232322333, 2232332233, 2323222333, 2332322233, 2333222323, 2333223223, 3223232323, 3232222333, 3232232233, 3232233223, 3232322323, 3323232223, 22222232333333, 22222322333333, 22222323233333
OFFSET
1,1
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
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) \\ Needs B() from A087510.
concat(vector(6, k, B(k, 2, 3, isprime))) \\ Andrew Howroyd, Sep 21 2024
CROSSREFS
KEYWORD
base,nonn
AUTHOR
EXTENSIONS
Offset changed to 1 and a(19) corrected by Georg Fischer, Jan 11 2022
STATUS
approved