A356898 a(n) is the number of trailing 1's in the maximal tribonacci representation of n (A352103).

0, 1, 0, 2, 0, 1, 0, 3, 1, 0, 2, 0, 1, 0, 4, 0, 2, 0, 1, 0, 3, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 3, 1, 0, 2, 0, 1, 0, 4, 0, 2, 0, 1, 0, 3, 1, 0, 2, 0, 1, 0, 6, 1, 0, 2, 0, 1, 0, 4, 0, 2, 0, 1, 0, 3, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 3, 1, 0, 2, 0, 1, 0, 4, 0, 2, 0, 1

Offset

0,4

Comments

The asymptotic density of the occurrences of k = 0, 1, 2, ... is (c-1)/c^(k+1), where c = 1.839286... (A058265) is the tribonacci constant.

The asymptotic mean of this sequence is 1/(c-1) = 1.191487...

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Example

  n  a(n)  A352103(n)
  -  ----  ----------
  0     0           0
  1     1           1
  2     0          10
  3     2          11
  4     0         100
  5     1         101
  6     0         110
  7     3         111
  8     1        1001
  9     0        1010

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]; a[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]]; Array[a, 100, 0]

Crossrefs

Cf. A058265, A352103, A356896, A356897.

Similar sequences: A278045, A356749.

Sequence in context: A363952 A245151 A243978 * A106844 A128618 A363904

Adjacent sequences: A356895 A356896 A356897 * A356899 A356900 A356901

Keyword

nonn,base

Author

Amiram Eldar, Sep 03 2022

Status

approved