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A383500 Positive integers that contain the digit 9, or an odd digit d immediately preceded by a digit <= d.

%I A383500 #17 May 11 2025 11:57:39
%S A383500 9,11,13,15,17,19,23,25,27,29,33,35,37,39,45,47,49,55,57,59,67,69,77,
%T A383500 79,89,90,91,92,93,94,95,96,97,98,99,101,103,105,107,109,110,111,112,
%U A383500 113,114,115,116,117,118,119,123,125,127,129,130,131,132,133,134,135,136,137
%N A383500 Positive integers that contain the digit 9, or an odd digit d immediately preceded by a digit <= d.
%C A383500 Conjecture: these are the numbers missing from A382935.
%C A383500 Theorem: This sequence is the complement of A382935. - _Quinn Savitt_, May 08 2025
%H A383500 Paolo Xausa, <a href="/A383500/b383500.txt">Table of n, a(n) for n = 1..10000</a>
%H A383500 Quinn Savitt, <a href="/A383500/a383500_1.pdf">Proof that A383500 is the Complement of A382935</a>
%t A383500 A383500Q[k_] := MemberQ[#, 9] || MemberQ[Partition[#, 2, 1], {i_, j_?OddQ} /; i <= j] & [IntegerDigits[k]];
%t A383500 Select[Range[200], A383500Q]
%o A383500 (Python)
%o A383500 def ok(n):
%o A383500     s = str(n)
%o A383500     return "9" in s or any(d in "13579" and s[i-1]<=d for i, d in enumerate(s) if i > 0)
%o A383500 print([k for k in range(134) if ok(k)]) # _Michael S. Branicky_, Apr 29 2025
%Y A383500 Cf. A382935, A383501 (complement).
%Y A383500 Cf. A347298, A382464, A382623, A382937, A383061, A383245, A383247, A383249.
%K A383500 nonn,base,easy
%O A383500 1,1
%A A383500 _Paolo Xausa_, Apr 29 2025