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

Author

Clark Kimberling, Feb 04 2023

Keywords

• nonn
• easy

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.

Examples

			(See A332938.)
		

Crossrefs

Cf. A000045, A035513, A332937, A332938.

Programs

Mathematica

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