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A383501 Nonnegative integers without the digit 9 such that every odd digit except the leftmost is immediately preceded by a larger digit.

%I A383501 #7 Apr 29 2025 13:39:57
%S A383501 0,1,2,3,4,5,6,7,8,10,12,14,16,18,20,21,22,24,26,28,30,31,32,34,36,38,
%T A383501 40,41,42,43,44,46,48,50,51,52,53,54,56,58,60,61,62,63,64,65,66,68,70,
%U A383501 71,72,73,74,75,76,78,80,81,82,83,84,85,86,87,88,100,102,104,106,108
%N A383501 Nonnegative integers without the digit 9 such that every odd digit except the leftmost is immediately preceded by a larger digit.
%C A383501 Conjecture: these are the terms of A382935, sorted.
%H A383501 Paolo Xausa, <a href="/A383501/b383501.txt">Table of n, a(n) for n = 1..10000</a>
%t A383501 A383501Q[k_] := FreeQ[#, 9] && FreeQ[Partition[#, 2, 1], {i_, j_?OddQ} /; i <= j] & [IntegerDigits[k]];
%t A383501 Select[Range[0, 200], A383501Q]
%o A383501 (Python)
%o A383501 def ok(n):
%o A383501     s = str(n)
%o A383501     return "9" not in s and all(d not in "13579" or s[i-1]>d for i, d in enumerate(s) if i > 0)
%o A383501 print([k for k in range(134) if ok(k)]) # _Michael S. Branicky_, Apr 29 2025
%Y A383501 Cf. A382935, A383500 (complement).
%Y A383501 Cf. A377912, A382465, A382624, A382938, A383062, A383246, A383248, A383250.
%K A383501 nonn,base,easy
%O A383501 1,3
%A A383501 _Paolo Xausa_, Apr 29 2025