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

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%I A360374 #6 Feb 04 2023 20:46:00
%S A360374 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 A360374 58,61,67,71,73,77,78,82,83,87,89,91,93,96,97,99,103,105,106,109,113,
%U A360374 115,119,121,125,129,130,135,136,137,139,141,145,151,153,154
%N A360374 Indices of the nonprimitive rows of the Wythoff array (A035513); see Comments.
%C A360374 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 A360374 (See A332938.)
%t A360374 W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];
%t A360374 Select[Range[200], GCD[W[#, 1], W[#, 2]] > 1 &]
%Y A360374 Cf. A000045, A035513, A332937, A332938.
%K A360374 nonn,easy
%O A360374 1,1
%A A360374 _Clark Kimberling_, Feb 04 2023