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Indices of the nonprimitive rows of the Wythoff array (A035513); see Comments.
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%I #6 Feb 04 2023 20:46:00

%S 3,4,5,9,13,15,16,19,22,25,28,29,31,34,35,41,43,45,47,51,52,55,56,57,

%T 58,61,67,71,73,77,78,82,83,87,89,91,93,96,97,99,103,105,106,109,113,

%U 115,119,121,125,129,130,135,136,137,139,141,145,151,153,154

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

%C 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.

%e (See A332938.)

%t W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];

%t Select[Range[200], GCD[W[#, 1], W[#, 2]] > 1 &]

%Y Cf. A000045, A035513, A332937, A332938.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Feb 04 2023