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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
Sequence in context: A322274 A008365 A132077 * A045921 A296520 A334391
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.)