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

%I A235154 #37 May 20 2025 21:33:48
%S A235154 13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,113,
%T A235154 131,151,181,191,199,211,223,227,229,233,277,311,313,331,337,353,373,
%U A235154 383,433,443,449,499,557,577,599,661,677,727,733,757,773,787,797,811
%N A235154 Primes which have one or more occurrences of exactly two different digits.
%C A235154 The first term having a repeated digit is 101.
%C A235154 a(3402) > 10^10.
%H A235154 Michael S. Branicky, <a href="/A235154/b235154.txt">Table of n, a(n) for n = 1..12000</a> (terms 651..3401 from Christopher M. Conrey, terms 1..650 from Colin Barker)
%H A235154 David A. Corneth, <a href="/A235154/a235154.gp.txt">PARI program</a>
%o A235154 (PARI) s=[]; forprime(n=10, 1000, if(#vecsort(eval(Vec(Str(n))),,8)==2, s=concat(s, n))); s
%o A235154 (PARI) is(n)=isprime(n) && #Set(digits(n))==2 \\ _Charles R Greathouse IV_, Feb 23 2017
%o A235154 (PARI) \\ See Corneth link
%o A235154 (Python)
%o A235154 from sympy import isprime
%o A235154 from sympy.utilities.iterables import multiset_permutations
%o A235154 from itertools import count, islice, combinations_with_replacement, product
%o A235154 def agen():
%o A235154     for digits in count(2):
%o A235154         s = set()
%o A235154         for pair in product("0123456789", "1379"):
%o A235154             if pair[0] == pair[1]: continue
%o A235154             for c in combinations_with_replacement(pair, digits):
%o A235154                 if len(set(c)) < 2 or sum(int(ci) for ci in c)%3 == 0:
%o A235154                     continue
%o A235154                 for p in multiset_permutations(c):
%o A235154                     if p[0] == "0": continue
%o A235154                     t = int("".join(p))
%o A235154                     if isprime(t):
%o A235154                         s.add(t)
%o A235154         yield from sorted(s)
%o A235154 print(list(islice(agen(), 100))) # _Michael S. Branicky_, Jan 23 2022
%Y A235154 Cf. A034845, A235155-A235161, A030291.
%K A235154 nonn,base
%O A235154 1,1
%A A235154 _Colin Barker_, Jan 04 2014