A255670 Number of the column of the Wythoff array (A035513) that contains L(n), where L = A000201, the lower Wythoff sequence.

1, 3, 1, 1, 5, 1, 3, 1, 1, 3, 1, 1, 7, 1, 3, 1, 1, 5, 1, 3, 1, 1, 3, 1, 1, 5, 1, 3, 1, 1, 3, 1, 1, 9, 1, 3, 1, 1, 5, 1, 3, 1, 1, 3, 1, 1, 7, 1, 3, 1, 1, 5, 1, 3, 1, 1, 3, 1, 1, 5, 1, 3, 1, 1, 3, 1, 1, 7, 1, 3, 1, 1, 5, 1, 3, 1, 1, 3, 1, 1, 5, 1, 3, 1, 1, 3

Offset

1,2

Comments

All the terms are odd, and every odd positive integer occurs infinitely many times.

Links

Table of n, a(n) for n=1..86.

Formula

a(n) = A225671(n) - 1 = A035612(A000201(n)).

a(n) = 1 if and only if n = L(j) for some j; otherwise, n = U(k) for some k.

Example

Corner of the Wythoff array:
1   2   3   5   8   13
4   7   11  18  29  47
6   10  16  26  42  68
9   15  24  39  63  102
L = (1,3,4,6,8,9,11,...); U = (2,5,7,10,13,15,18,...), so that
A255670 = (1,3,1,1,5,...) and A255671 = (2,4,2,2,6,...).

Mathematica

z = 13; r = GoldenRatio; f[1] = {1}; f[2] = {1, 2};
f[n_] := f[n] = Join[f[n - 1], Most[f[n - 2]], {n}]; f[z];
g[n_] := g[n] = f[z][[n]]; Table[g[n], {n, 1, 100}]  (* A035612 *)
Table[g[Floor[n*r]], {n, 1, (1/r) Length[f[z]]}]     (* A255670 *)
Table[g[Floor[n*r^2]], {n, 1, (1/r^2) Length[f[z]]}] (* A255671 *)

Crossrefs

Cf. A255671, A035612, A000201, A001950.

Sequence in context: A184726 A046230 A046229 * A182469 A329984 A261697

Adjacent sequences: A255667 A255668 A255669 * A255671 A255672 A255673

Keyword

nonn,easy

Author

Clark Kimberling, Mar 03 2015

Status

approved