A356894 - OEIS

A356894

a(n) is the number of 0's in the maximal tribonacci representation of n (A352103).

1, 0, 1, 0, 2, 1, 1, 0, 2, 2, 1, 2, 1, 1, 0, 3, 2, 3, 2, 2, 1, 2, 2, 1, 2, 1, 1, 0, 4, 3, 3, 2, 3, 3, 2, 3, 2, 2, 1, 3, 2, 3, 2, 2, 1, 2, 2, 1, 2, 1, 1, 0, 4, 4, 3, 4, 3, 3, 2, 4, 3, 4, 3, 3, 2, 3, 3, 2, 3, 2, 2, 1, 4, 3, 3, 2, 3, 3, 2, 3, 2, 2, 1, 3, 2, 3, 2

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

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

FORMULA

a(n) = A356895(n) - A352104(n).

EXAMPLE

n a(n) A352103(n)

- ---- ----------

0 1 0

1 0 1

2 1 10

3 0 11

4 2 100

5 1 101

6 1 110

7 0 111

8 2 1001

9 2 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, Count[v[[i[[1, 1]] ;; -1]], 0]]]; Array[a, 100, 0]

CROSSREFS

Cf. A000073, A352103, A352104, A356895.

Similar sequences: A023416, A102364, A117479, A278042.

Sequence in context: A025860 A322285 A152487 * A338019 A058394 A353366

Adjacent sequences: A356891 A356892 A356893 * A356895 A356896 A356897

KEYWORD

nonn,base

AUTHOR

Amiram Eldar, Sep 03 2022

STATUS

approved