A235154 Primes which have one or more occurrences of exactly two different digits.

13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 113, 131, 151, 181, 191, 199, 211, 223, 227, 229, 233, 277, 311, 313, 331, 337, 353, 373, 383, 433, 443, 449, 499, 557, 577, 599, 661, 677, 727, 733, 757, 773, 787, 797, 811

Offset: 1

Author

Colin Barker, Jan 04 2014

Keywords

• nonn
• base

Comments

The first term having a repeated digit is 101.

a(3402) > 10^10.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..12000 (terms 651..3401 from Christopher M. Conrey, terms 1..650 from Colin Barker)
• David A. Corneth, PARI program

Crossrefs

Cf. A034845, A235155-A235161, A030291.

Programs

PARI

s=[]; forprime(n=10, 1000, if(#vecsort(eval(Vec(Str(n))),,8)==2, s=concat(s, n))); s

PARI

is(n)=isprime(n) && #Set(digits(n))==2 \\ Charles R Greathouse IV, Feb 23 2017

PARI

\\ See Corneth link

Python

from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
from itertools import count, islice, combinations_with_replacement, product
def agen():
    for digits in count(2):
        s = set()
        for pair in product("0123456789", "1379"):
            if pair[0] == pair[1]: continue
            for c in combinations_with_replacement(pair, digits):
                if len(set(c)) < 2 or sum(int(ci) for ci in c)%3 == 0:
                    continue
                for p in multiset_permutations(c):
                    if p[0] == "0": continue
                    t = int("".join(p))
                    if isprime(t):
                        s.add(t)
        yield from sorted(s)
print(list(islice(agen(), 100))) # Michael S. Branicky, Jan 23 2022