A352104 a(n) is the number of 1's in the maximal tribonacci representation of n (A352103).

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

Offset

0,4

Links

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

Formula

a(n) = A007953(A352103(n)).

a(n) >= A278043(n).

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 == {}, 0, Total[v[[i[[1, 1]] ;; -1]]]]]; Array[a, 100, 0]

Crossrefs

Cf. A000073, A007953, A352103.

Similar sequences: A000120, A007895, A112310, A278043.

Sequence in context: A096004 A193495 A071068 * A240872 A328806 A326370

Adjacent sequences: A352101 A352102 A352103 * A352105 A352106 A352107

Keyword

nonn,base

Author

Amiram Eldar, Mar 05 2022

Status

approved