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A382935 Lexicographically earliest sequence of distinct nonnegative integers such that if a digit d in the digit stream (ignoring commas) is odd, the previous digit is > d.

%I A382935 #22 Apr 30 2025 11:09:50
%S A382935 0,2,1,4,3,6,5,8,7,10,20,21,22,12,14,16,18,24,26,28,30,40,41,42,43,44,
%T A382935 31,46,32,48,34,36,38,50,60,61,62,63,64,65,66,51,68,52,80,81,82,83,84,
%U A382935 85,86,53,87,54,88,56,58,70,200,202,100,204,102,104,106,108,71,206,120,208
%N A382935 Lexicographically earliest sequence of distinct nonnegative integers such that if a digit d in the digit stream (ignoring commas) is odd, the previous digit is > d.
%C A382935 Could be summarized as "odd digit, previous bigger". A variant of A342042.
%C A382935 No term contains the digit 9.
%H A382935 Paolo Xausa, <a href="/A382935/b382935.txt">Table of n, a(n) for n = 1..10000</a>
%H A382935 Paolo Xausa, <a href="/A382935/a382935.png">Color scatterplot of the first 50000 terms</a>
%t A382935 A382935list[nmax_] := Module[{a, s, invQ, fu = 1},
%t A382935   invQ[k_] := invQ[k] = (If[#, s[k] = #]; #) & [MemberQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?OddQ} /; i <= j]];
%t A382935   s[_] := False; s[0] = True;
%t A382935   NestList[(a = fu; While[s[a] || invQ[a] || invQ[# + First[IntegerDigits[a]]], a++] & [Max[Mod[#, 10], 1]*10]; While[s[fu], fu++]; s[a] = True; a) &, 0, nmax - 1]];
%t A382935 A382935list[100]
%o A382935 (Python)
%o A382935 from itertools import count, islice
%o A382935 def cond(s):
%o A382935     return all(s[i+1] < s[i] for i in range(len(s)-1) if s[i+1] in "13579")
%o A382935 def agen(): # generator of terms
%o A382935     an, seen, s, m = 0, {0}, "0", 1
%o A382935     while True:
%o A382935         yield an
%o A382935         an = next(k for k in count(m) if k not in seen and cond(s[-1]+str(k)))
%o A382935         seen.add(an); s += str(an)
%o A382935         while m in seen or not cond(str(m)): m += 1
%o A382935 print(list(islice(agen(), 70))) # _Michael S. Branicky_, Apr 14 2025
%Y A382935 Similar sequences: A342042, A342043, A342044, A342045, A382462, A382621, A383059.
%Y A382935 Cf. A382936, A382939, A383500, A383501.
%K A382935 nonn,base,look
%O A382935 1,2
%A A382935 _Paolo Xausa_, Apr 14 2025