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

1,2

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.

Links

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

Example

   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

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[#]] &]

Crossrefs

Complement of A356897.

Cf. A058265, A352103, A356898.

Similar sequences: A308197, A342051.

Sequence in context: A047419 A135205 A145733 * A111251 A047300 A026439

Adjacent sequences: A356893 A356894 A356895 * A356897 A356898 A356899

Keyword

nonn,base

Author

Amiram Eldar, Sep 03 2022

Status

approved