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A382462 Lexicographically earliest sequence of distinct positive integers such that if a digit d in the digit stream (ignoring commas) is even, the previous digit is < d.

%I A382462 #25 May 13 2025 11:34:11
%S A382462 1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,31,21,23,33,34,35,36,37,
%T A382462 38,39,51,24,53,41,25,55,56,57,58,59,71,26,73,43,45,61,27,75,63,46,77,
%U A382462 78,79,91,28,93,47,81,29,95,65,67,83,48,97,85,68,99,111,49,112,69
%N A382462 Lexicographically earliest sequence of distinct positive integers such that if a digit d in the digit stream (ignoring commas) is even, the previous digit is < d.
%C A382462 Could be summarized as "even digit, previous smaller". A variant of A342042.
%C A382462 No term contains the digit 0. - _Paolo Xausa_, Apr 30 2025
%H A382462 Paolo Xausa, <a href="/A382462/b382462.txt">Table of n, a(n) for n = 1..10000</a>
%t A382462 A382462list[nmax_] := Module[{a, s, invQ, fu = 2},
%t A382462   invQ[k_] := invQ[k] = (If[#, s[k] = #]; #) & [MemberQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?EvenQ} /; i >= j]];
%t A382462   s[_] := False; s[1] = True;
%t A382462   NestList[(a = fu; While[s[a] || invQ[a] || invQ[# + First[IntegerDigits[a]]], a++] & [Mod[#, 10]*10]; While[s[fu], fu++]; s[a] = True; a) &, 1, nmax-1]];
%t A382462 A382462list[100]
%o A382462 (Python)
%o A382462 from itertools import count, islice
%o A382462 def cond(s):
%o A382462     return all(s[i] > s[i-1] for i in range(1, len(s)) if s[i] in "02468")
%o A382462 def agen(): # generator of terms
%o A382462     an, seen, s, m = 1, {1}, "1", 1
%o A382462     while True:
%o A382462         yield an
%o A382462         an = next(k for k in count(m) if k not in seen and cond(s[-1]+str(k)))
%o A382462         seen.add(an); s += str(an)
%o A382462         while m in seen or not cond(str(m)): m += 1
%o A382462 print(list(islice(agen(), 70))) # _Michael S. Branicky_, Apr 19 2025
%Y A382462 Similar sequences: A342042, A342043, A342044, A342045, A382621, A382935, A383059.
%Y A382462 Cf. A382463, A382464, A382465, A382466.
%K A382462 nonn,base,look
%O A382462 1,2
%A A382462 _Paolo Xausa_, Mar 27 2025