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A383249 Positive integers ending with the digit 1, or containing an odd digit d immediately followed by a digit >= d.

%I A383249 #16 May 05 2025 22:57:03
%S A383249 1,11,12,13,14,15,16,17,18,19,21,31,33,34,35,36,37,38,39,41,51,55,56,
%T A383249 57,58,59,61,71,77,78,79,81,91,99,101,110,111,112,113,114,115,116,117,
%U A383249 118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135
%N A383249 Positive integers ending with the digit 1, or containing an odd digit d immediately followed by a digit >= d.
%C A383249 Conjecture: these are the numbers missing from A342045.
%C A383249 By way of disjointness and completeness, it is proved that this sequence is the complement of A342045. - _Quinn Savitt_, Apr 29 2025
%H A383249 Paolo Xausa, <a href="/A383249/b383249.txt">Table of n, a(n) for n = 1..10000</a>
%H A383249 Quinn Savitt, <a href="/A383249/a383249.pdf">Proof that A383249 is the complement of A342045</a>
%t A383249 A383249Q[k_] := Last[#] == 1 || MemberQ[Partition[#, 2, 1], {i_?OddQ, j_} /; j >= i] & [IntegerDigits[k]];
%t A383249 Select[Range[200], A383249Q]
%o A383249 (Python)
%o A383249 def ok(n):
%o A383249     if n%10 == 1: return True
%o A383249     s = str(n)
%o A383249     return any(d in "13579" and s[i]>=d for i, d in enumerate(s, 1) if i < len(s))
%o A383249 print([k for k in range(136) if ok(k)]) # _Michael S. Branicky_, Apr 28 2025
%Y A383249 Cf. A342045, A383250 (complement).
%Y A383249 Cf. A347298, A382464, A382623, A382937, A383061, A383245, A383247.
%K A383249 nonn,base,easy
%O A383249 1,2
%A A383249 _Paolo Xausa_, Apr 26 2025