A356897 - OEIS

%I #8 Sep 05 2022 05:24:50

%S 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 71,73,75,76,80,86,88,89,93,95,99,101,102,106,108,110,112,113,117,123,

%U 125,126,130,133,137,143,145,146,150,152,154,156,157,161,167,169

%N Nonnegative numbers whose maximal tribonacci representation (A352103) ends in an odd number of 1's.

%C Numbers k such that A356898(k) is odd.

%C The asymptotic density of this sequence is 1/(c+1) = 0.352201..., where c = 1.839286... (A058265) is the tribonacci constant.

%H Amiram Eldar, <a href="/A356897/b356897.txt">Table of n, a(n) for n = 1..10000</a>

%e    n  a(n)  A352103(n)  A356898(n)

%e    -  ----  ----------  ----------

%e    1     1           1          1

%e    2     5         101          1

%e    3     7         111          3

%e    4     8        1001          1

%e    5    12        1101          1

%e    6    18       10101          1

%e    7    20       10111          3

%e    8    21       11001          1

%e    9    25       11101          1

%e   10    27       11111          5

%t 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 Complement of A356896.

%Y Cf. A058265, A352103, A356898.

%Y Similar sequences: A001950, A308198, A342050.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Sep 03 2022