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A255670 Number of the column of the Wythoff array (A035513) that contains L(n), where L = A000201, the lower Wythoff sequence. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A261697 A261698

Adjacent sequences:  A255667 A255668 A255669 * A255671 A255672 A255673

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 03 2015

STATUS

approved

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Last modified November 21 15:00 EST 2019. Contains 329371 sequences. (Running on oeis4.)