cp's OEIS Frontend

A302500 Lexicographically first sequence of distinct terms such that any set of five successive digits can be reordered as {d, d+1, d+2, d+3, d+4}, d being the smallest of the five digits.

%I A302500 #11 Feb 03 2025 21:24:12
%S A302500 0,1,2,3,4,5,6,7,8,9,56,78,45,67,34,562,345,12,340,123,40,1234,51,23,
%T A302500 401,234,512,3401,2340,12340,12345,62,3451,2345,623,451,23401,23451,
%U A302500 23456,73,456,734,567,84,5673,4562,3456,784,5678,95,678,956,789,56784,56734,5623,4512,34012,34512,34562,34567,89
%N A302500 Lexicographically first sequence of distinct terms such that any set of five successive digits can be reordered as {d, d+1, d+2, d+3, d+4}, d being the smallest of the five digits.
%C A302500 As the digit 0 has no predecessor and the digit 9 has no successor here, sets of successive digits like {3,2,1,0,9} and {6,7,8,9,0} are forbidden.
%H A302500 Dominic McCarty, <a href="/A302500/b302500.txt">Table of n, a(n) for n = 1..10000</a> (first 257 terms from Jean-Marc Falcoz)
%e A302500 Terms a(1) to a(10) are obvious;
%e A302500 a(11) is 56 because 56 is the smallest integer not yet in the sequence such that the elements of the sets {6,7,8,9,5} and {7,8,9,5,6} are five consecutive digits;
%e A302500 a(12) is 78 because 78 is the smallest integer not yet in the sequence such that the elements of the sets {8,9,5,6,7} and {9,5,6,7,8} are five consecutive digits;
%e A302500 a(13) is 45 because 45 is the smallest integer not yet in the sequence such that the elements of the sets {5,6,7,8,4} and {6,7,8,4,5} are five consecutive digits;
%e A302500 etc.
%o A302500 (Python)
%o A302500 a, runLength = [i for i in range(10)], 5
%o A302500 def helper(s, k, l, a):
%o A302500     if k not in a: return k
%o A302500     return min([helper(s[(2-l):]+str(i), int(str(k)+str(i)), l, a) for i in range(10) if (k!=0 or i!=0) and s.find(str(i))==-1 and (all(d[n]+1==d[n+1] for n in range(l-1)) if (d:=sorted([int((s+str(i))[n]) for n in range(l)])) else False)])
%o A302500 while len(a)<100: a.append(helper(("".join(map(str, a)))[(1-runLength):], 0, runLength, a))
%o A302500 print(a) # _Dominic McCarty_, Feb 03 2025
%Y A302500 Cf. A228326 for the same idea with sets of two digits, A302173 for sets of three digits and A302499 for sets of four digits.
%K A302500 nonn,base
%O A302500 1,3
%A A302500 _Eric Angelini_ and _Jean-Marc Falcoz_, Apr 09 2018