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A383059 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 A383059 #9 Apr 19 2025 18:02:13
%S A383059 0,1,2,3,4,5,6,7,8,9,20,10,12,22,23,24,25,26,27,28,29,40,13,42,30,14,
%T A383059 44,45,46,47,48,49,60,15,62,32,34,50,16,64,52,35,66,67,68,69,80,17,82,
%U A383059 36,70,18,84,54,56,72,37,86,74,57,88,89,200,19,201,38,90,39,202,58
%N A383059 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 A383059 Could be summarized as "odd digit, previous smaller". A variant of A342042.
%H A383059 Paolo Xausa, <a href="/A383059/b383059.txt">Table of n, a(n) for n = 1..10000</a>
%H A383059 Paolo Xausa, <a href="/A383059/a383059.png">Color scatterplot of the first 100000 terms</a>
%t A383059 A383059list[nmax_] := Module[{a, s, invQ, fu = 1},
%t A383059   invQ[k_] := invQ[k] = (If[#, s[k] = #]; #) & [MemberQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?OddQ} /; i >= j]];
%t A383059   s[_] := False; s[0] = True;
%t A383059   NestList[(a = fu; While[s[a] || invQ[a] || invQ[# + First[IntegerDigits[a]]], a++] & [Mod[#, 10]*10]; While[s[fu], fu++]; s[a] = True; a) &, 0, nmax - 1]];
%t A383059 A383059list[100]
%o A383059 (Python)
%o A383059 from itertools import count, islice
%o A383059 def cond(s):
%o A383059     return all(s[i] > s[i-1] for i in range(1, len(s)) if s[i] in "13579")
%o A383059 def agen(): # generator of terms
%o A383059     an, seen, s, m = 0, {0}, "0", 1
%o A383059     while True:
%o A383059         yield an
%o A383059         an = next(k for k in count(m) if k not in seen and cond(s[-1]+str(k)))
%o A383059         seen.add(an); s += str(an)
%o A383059         while m in seen or not cond(str(m)): m += 1
%o A383059 print(list(islice(agen(), 70))) # _Michael S. Branicky_, Apr 19 2025
%Y A383059 Similar sequences: A342042, A342043, A342044, A342045, A382462, A382621, A382935.
%Y A383059 Cf. A383060, A383061, A383062, A383063.
%K A383059 nonn,base,look
%O A383059 1,3
%A A383059 _Paolo Xausa_, Apr 18 2025