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

1,1

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

Prog

(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

Crossrefs

Cf. A235155-A235161, A030291.

Sequence in context: A322274 A008365 A132077 * A045921 A296520 A334391

Adjacent sequences: A235151 A235152 A235153 * A235155 A235156 A235157

Keyword

nonn,base

Author

Colin Barker, Jan 04 2014

Status

approved