login
A356895
a(n) is the length of the maximal tribonacci representation of n (A352103).
3
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
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
Similar sequences: A070939, A072649, A095791, A278044.
Sequence in context: A070939 A113473 A265370 * A238407 A196050 A334097
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Sep 03 2022
STATUS
approved