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A331975 Lexicographically earliest sequence of distinct positive integers such that three successive digits are always distinct.

%I A331975 #18 Jul 01 2022 05:33:36
%S A331975 1,2,3,4,5,6,7,8,9,10,21,30,12,31,20,13,24,15,23,14,25,16,27,18,26,17,
%T A331975 28,19,32,40,29,34,50,35,41,36,42,37,43,51,38,45,39,46,52,47,53,48,54,
%U A331975 60,49,56,70,57,61,58,62,59,63,71,64,72,65,73,67,80,68,74,69,75,81,76,82,78,90,79,83,91,84
%N A331975 Lexicographically earliest sequence of distinct positive integers such that three successive digits are always distinct.
%H A331975 Carole Dubois, <a href="/A331975/b331975.txt">Table of n, a(n) for n = 1..5000</a>
%e A331975 As a(10) = 10, a(11) cannot start with a 1 or have a 0 in second position; thus a(11) = 21;
%e A331975 as a(11) = 21, a(12) cannot start with a 1 or a 2; thus a(12) = 30;
%e A331975 as a(12) = 30, a(13) = 12, smallest available integer not leading to an immediate contradiction;
%e A331975 as a(13) = 12, a(14) cannot start with 1 or 2; thus a(14) = 31, smallest available integer not leading to an immediate contradiction. Etc.
%o A331975 (Python)
%o A331975 from itertools import islice
%o A331975 def ok(s): return all(len(set(s[i:i+3]))==3 for i in range(len(s)-2))
%o A331975 def agen(): # generator of terms
%o A331975     aset, s, k, mink = {1}, "x1", 1, 2
%o A331975     while True:
%o A331975         yield k
%o A331975         k, avoid = mink, set(s)
%o A331975         while k in aset or not ok(s + str(k)): k += 1
%o A331975         aset.add(k)
%o A331975         s = (s + str(k))[-3:]
%o A331975         while mink in aset: mink += 1
%o A331975 print(list(islice(agen(), 79))) # _Michael S. Branicky_, Jun 30 2022
%Y A331975 Cf. A331215 (a variant with 4 successive distinct digits instead of 3).
%K A331975 base,nonn
%O A331975 1,2
%A A331975 _Eric Angelini_ and _Carole Dubois_, Feb 03 2020