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 A235154 Primes which have one or more occurrences of exactly two different digits. 22
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 29 05:33 EDT 2024. Contains 372921 sequences. (Running on oeis4.)