This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A356897 #8 Sep 05 2022 05:24:50
%S A356897 1,5,7,8,12,18,20,21,25,27,29,31,32,36,42,44,45,49,52,56,62,64,65,69,
%T A356897 71,73,75,76,80,86,88,89,93,95,99,101,102,106,108,110,112,113,117,123,
%U A356897 125,126,130,133,137,143,145,146,150,152,154,156,157,161,167,169
%N A356897 Nonnegative numbers whose maximal tribonacci representation (A352103) ends in an odd number of 1's.
%C A356897 Numbers k such that A356898(k) is odd.
%C A356897 The asymptotic density of this sequence is 1/(c+1) = 0.352201..., where c = 1.839286... (A058265) is the tribonacci constant.
%H A356897 Amiram Eldar, <a href="/A356897/b356897.txt">Table of n, a(n) for n = 1..10000</a>
%e A356897 n a(n) A352103(n) A356898(n)
%e A356897 - ---- ---------- ----------
%e A356897 1 1 1 1
%e A356897 2 5 101 1
%e A356897 3 7 111 3
%e A356897 4 8 1001 1
%e A356897 5 12 1101 1
%e A356897 6 18 10101 1
%e A356897 7 20 10111 3
%e A356897 8 21 11001 1
%e A356897 9 25 11101 1
%e A356897 10 27 11111 5
%t A356897 t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; trib[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[t[k] <= m, k++]; k--; AppendTo[s, k]; m -= t[k]; k = 1]; IntegerDigits[Total[2^(s - 1)], 2]]; f[v_] := Module[{m = Length[v], k}, k = m; While[v[[k]] == 1, k--]; m - k]; c[n_] := Module[{v = trib[n]}, nv = Length[v]; i = 1; While[i <= nv - 3, If[v[[i ;; i + 3]] == {1, 0, 0, 0}, v[[i ;; i + 3]] = {0, 1, 1, 1}; If[i > 3, i -= 4]]; i++]; i = Position[v, _?(# > 0 &)]; If[i == {}, 0, f[v[[i[[1, 1]] ;; -1]]], 10]]; Select[Range[0, 200], OddQ[c[#]] &]
%Y A356897 Complement of A356896.
%Y A356897 Cf. A058265, A352103, A356898.
%Y A356897 Similar sequences: A001950, A308198, A342050.
%K A356897 nonn,base
%O A356897 1,2
%A A356897 _Amiram Eldar_, Sep 03 2022