A356896 Nonnegative numbers whose maximal tribonacci representation (A352103) ends in an even number of 1's.

0, 2, 3, 4, 6, 9, 10, 11, 13, 14, 15, 16, 17, 19, 22, 23, 24, 26, 28, 30, 33, 34, 35, 37, 38, 39, 40, 41, 43, 46, 47, 48, 50, 51, 53, 54, 55, 57, 58, 59, 60, 61, 63, 66, 67, 68, 70, 72, 74, 77, 78, 79, 81, 82, 83, 84, 85, 87, 90, 91, 92, 94, 96, 97, 98, 100, 103

Offset: 1

Author

Amiram Eldar, Sep 03 2022

Keywords

• nonn
• base

Comments

Numbers k such that A356898(k) is even.

The asymptotic density of this sequence is c/(c+1) = 0.647798..., where c = 1.839286... (A058265) is the tribonacci constant.

Examples

			   n  a(n)  A352103(n)  A356898(n)
   -  ----  ----------  ----------
   1     0           0          0
   2     2          10          0
   3     3          11          2
   4     4         100          0
   5     6         110          0
   6     9        1010          0
   7    10        1011          2
   8    11        1100          0
   9    13        1110          0
  10    14        1111          4
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Complement of A356897.

Cf. A058265, A352103, A356898.

Similar sequences: A308197, A342051.

Programs

Mathematica

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, 100], EvenQ[c[#]] &]