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A383248 Nonnegative integers without the digit 9 such that every odd digit except the rightmost is immediately followed by a larger digit.

%I A383248 #9 Apr 28 2025 12:20:08
%S A383248 0,1,2,3,4,5,6,7,8,12,13,14,15,16,17,18,20,21,22,23,24,25,26,27,28,34,
%T A383248 35,36,37,38,40,41,42,43,44,45,46,47,48,56,57,58,60,61,62,63,64,65,66,
%U A383248 67,68,78,80,81,82,83,84,85,86,87,88,120,121,122,123,124,125,126,127,128
%N A383248 Nonnegative integers without the digit 9 such that every odd digit except the rightmost is immediately followed by a larger digit.
%C A383248 Conjecture: these are the terms of A342044, sorted.
%H A383248 Paolo Xausa, <a href="/A383248/b383248.txt">Table of n, a(n) for n = 1..10000</a>
%t A383248 A383248Q[k_] := FreeQ[#, 9] && FreeQ[Partition[#, 2, 1], {i_?OddQ, j_} /; j <= i] & [IntegerDigits[k]];
%t A383248 Select[Range[0, 200], A383248Q]
%o A383248 (Python)
%o A383248 def ok(n):
%o A383248     s = str(n)
%o A383248     return "9" not in s and all(d not in "13579" or s[i]>d for i, d in enumerate(s, 1) if i < len(s))
%o A383248 print([k for k in range(129) if ok(k)]) # _Michael S. Branicky_, Apr 28 2025
%Y A383248 Cf. A342044, A383247 (complement).
%Y A383248 Cf. A377912, A382465, A382624, A382938, A383062, A383246, A383250.
%K A383248 nonn,base,easy
%O A383248 1,3
%A A383248 _Paolo Xausa_, Apr 25 2025