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A331215 Lexicographically earliest sequence of distinct positive integers such that four successive digits are always distinct.

%I A331215 #33 Jul 01 2022 05:33:38
%S A331215 1,2,3,4,5,6,7,8,9,10,23,14,20,13,24,15,26,17,25,16,27,18,29,30,12,34,
%T A331215 19,28,31,40,21,35,41,32,45,36,42,37,46,38,47,39,48,50,43,51,49,52,60,
%U A331215 53,61,54,62,57,63,58,64,59,67,80,56,70,81,65,71,68,72,69,73,82,74,83,75,84,76,85,79,86,102
%N A331215 Lexicographically earliest sequence of distinct positive integers such that four successive digits are always distinct.
%C A331215 This is not A276766, though the first 63 terms are the same.
%H A331215 Carole Dubois, <a href="/A331215/b331215.txt">Table of n, a(n) for n = 1..5000</a>
%e A331215 The four digits of a(11) = 23 and a(12) = 14 are distinct;
%e A331215 the four digits of a(12) = 14 and a(13) = 20 are distinct;
%e A331215 but so are also the successive digits 3,1,4,2 visible in 23, 14, 20;
%e A331215 the four digits of a(13) = 20 and a(14) = 13 are distinct;
%e A331215 the four digits of a(14) = 13 and a(15) = 24 are distinct;
%e A331215 but so are also the successive digits 0,1,3,2 visible in 20,13,24; etc.
%o A331215 (Python)
%o A331215 from itertools import islice
%o A331215 def ok(s): return all(len(set(s[i:i+4]))==4 for i in range(len(s)-3))
%o A331215 def agen(): # generator of terms
%o A331215     aset, s, k, mink = {1}, "xy1", 1, 2
%o A331215     while True:
%o A331215         yield k
%o A331215         k, avoid = mink, set(s)
%o A331215         while k in aset or not ok(s + str(k)): k += 1
%o A331215         aset.add(k)
%o A331215         s = (s + str(k))[-4:]
%o A331215         while mink in aset: mink += 1
%o A331215 print(list(islice(agen(), 79))) # _Michael S. Branicky_, Jun 30 2022
%Y A331215 Cf. A331975 (a variant with 3 successive distinct digits instead of 4), A276766.
%K A331215 base,nonn
%O A331215 1,2
%A A331215 _Eric Angelini_ and _Carole Dubois_, Feb 03 2020