A360374 Indices of the nonprimitive rows of the Wythoff array (A035513); see Comments.

3, 4, 5, 9, 13, 15, 16, 19, 22, 25, 28, 29, 31, 34, 35, 41, 43, 45, 47, 51, 52, 55, 56, 57, 58, 61, 67, 71, 73, 77, 78, 82, 83, 87, 89, 91, 93, 96, 97, 99, 103, 105, 106, 109, 113, 115, 119, 121, 125, 129, 130, 135, 136, 137, 139, 141, 145, 151, 153, 154

Offset

1,1

Comments

In a row of the Wythoff array, either every two consecutive terms are relatively prime or else no two consecutive terms are relatively prime. In the first case, we call the row primitive, as in A332938. Otherwise, the row is an integer multiple of a tail of a preceding row, and we call the row nonprimitive. Conjecture: the limiting proportion of nonprimitive rows exists and is approximately 0.392.

Links

Table of n, a(n) for n=1..60.

Example

(See A332938.)

Mathematica

W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];
Select[Range[200], GCD[W[#, 1], W[#, 2]] > 1 &]

Crossrefs

Cf. A000045, A035513, A332937, A332938.

Sequence in context: A338256 A237132 A080633 * A242800 A136259 A099560

Adjacent sequences: A360371 A360372 A360373 * A360375 A360376 A360377

Keyword

nonn,easy

Author

Clark Kimberling, Feb 04 2023

Status

approved