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A377912 Numbers such that every even digit except the last is immediately followed by a strictly larger digit.

%I A377912 #43 Jul 09 2025 05:07:15
%S A377912 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,23,24,25,26,27,28,
%T A377912 29,30,31,32,33,34,35,36,37,38,39,45,46,47,48,49,50,51,52,53,54,55,56,
%U A377912 57,58,59,67,68,69,70,71,72,73,74,75,76,77,78,79,89,90,91,92,93,94,95,96,97,98,99,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117
%N A377912 Numbers such that every even digit except the last is immediately followed by a strictly larger digit.
%C A377912 In other words, numbers that do not contain a pair of successive digits i, j where i is even and j <= i.
%H A377912 Paolo Xausa, <a href="/A377912/b377912.txt">Table of n, a(n) for n = 1..10000</a>
%H A377912 Sela Fried, <a href="https://arxiv.org/abs/2505.14196">Even-up words and their variants</a>, arXiv:2505.14196 [math.CO], 2025.
%t A377912 A377912Q[k_] := FreeQ[Partition[IntegerDigits[k], 2, 1], {i_?EvenQ, j_} /; j <= i];
%t A377912 Select[Range[0, 200], A377912Q] (* _Paolo Xausa_, Mar 17 2025 *)
%o A377912 (Python)
%o A377912 def ok(n):
%o A377912     s = str(n)
%o A377912     return not any(s[i] in "2468" and s[i+1] <= s[i] for i in range(len(s)-1))
%o A377912 print([k for k in range(0, 118) if ok(k)]) # _Michael S. Branicky_, Nov 28 2024
%Y A377912 The complement of A347298. Cf. A342042, A377914, A377917, A377918.
%K A377912 nonn,base
%O A377912 1,3
%A A377912 _N. J. A. Sloane_, Nov 27 2024, with thanks to _Paolo Xausa_ for correcting the initial definition
%E A377912 Added 0 to match A342042, and replaced negative definition by a positive one. - _N. J. A. Sloane_, Nov 29 2024