A356895 a(n) is the length of the maximal tribonacci representation of n (A352103).

1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset

0,3

Links

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

Formula

a(n) = A352104(n) + A356894(n).

a(n) ~ log(n)/log(c), where c is the tribonacci constant (A058265).

Example

  n  a(n)  A352103(n)
  -  ----  ----------
  0     1           0
  1     1           1
  2     2          10
  3     2          11
  4     3         100
  5     3         101
  6     3         110
  7     3         111
  8     4        1001
  9     4        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]]; 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 == {}, 1, Length[v[[i[[1, 1]] ;; -1]]]]]; Array[a, 100, 0]

Crossrefs

Cf. A352103, A352104, A356894.

Similar sequences: A070939, A072649, A095791, A278044.

Sequence in context: A070939 A113473 A265370 * A238407 A196050 A334097

Adjacent sequences: A356892 A356893 A356894 * A356896 A356897 A356898

Keyword

nonn,base

Author

Amiram Eldar, Sep 03 2022

Status

approved