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A363490 Lexicographically earliest infinite sequence of distinct terms > 0 such that one digit of a(n) is strictly smaller than one digit of a(n+1).

%I A363490 #19 Jun 24 2023 13:28:08
%S A363490 1,2,3,4,5,6,7,8,19,12,13,14,15,16,17,18,20,10,11,21,22,23,24,25,26,
%T A363490 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%U A363490 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70
%N A363490 Lexicographically earliest infinite sequence of distinct terms > 0 such that one digit of a(n) is strictly smaller than one digit of a(n+1).
%H A363490 Michael S. Branicky, <a href="/A363490/b363490.txt">Table of n, a(n) for n = 1..10000</a>
%e A363490 Digit 1 is < 2; 2 is < 3; etc. Then comes 8: if we write 9 after 8, the sequence stops (as there is no digit > 9). This forces a(9) = 19 (instead of 9) as the smallest available integer not leading to a contradiction. Integers consisting only of 9s (9, 99, 999, etc.) will thus never be part of the sequence.
%o A363490 (Python)
%o A363490 from itertools import islice
%o A363490 def agen(): # generator of terms
%o A363490     an, aset, mink = 1, {1}, 2
%o A363490     while True:
%o A363490         yield an
%o A363490         k, m = mink, min(str(an))
%o A363490         while k in aset or (s:=set(str(k))) == {"9"} or max(s) <= m:
%o A363490             k += 1
%o A363490         an = k
%o A363490         aset.add(an)
%o A363490         while mink in aset or set(str(mink)) == {"9"}:
%o A363490             aset.discard(mink); mink += 1
%o A363490 print(list(islice(agen(), 70))) # _Michael S. Branicky_, Jun 05 2023
%Y A363490 Cf. A294069.
%K A363490 base,nonn
%O A363490 1,2
%A A363490 _Eric Angelini_, Jun 05 2023