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A387351 Positions of -1's in A387348.

%I A387351 #5 Sep 01 2025 22:09:27
%S A387351 3,8,16,21,24,29,37,42,45,50,55,58,63,71,76,79,84,92,97,105,110,113,
%T A387351 118,126,131,134,139,144,147,152,160,165,168,173,181,186,194,199,202,
%U A387351 207,215,220,223,228,236,241,249,254,257,262,270,275,278,283,288,291
%N A387351 Positions of -1's in A387348.
%C A387351 This sequence together with A387349 and A387350 partition the positive integers.
%C A387351 Conjecture: the difference sequence, (5, 8, 5, 3, 5, 8, 5, 3, 5, 5, 3, 5, 8, 5, 3, 5, 8, 5, 8, ... ) has exactly 3 distinct terms.
%t A387351 z = 300;
%t A387351 A[n_, k_] := Module[{t, a, b}, t = (1 + Sqrt[5])/2;
%t A387351 a = Floor[n*(t + 1) + 1 + t/2]; b = Round[a*t]; ({b, a} . MatrixPower[{{1, 1}, {1, 0}}, k])[[2]]];
%t A387351 ts = Table[A[n, k], {n, 0, z - 1}, {k, 0, z - 1}];  (* A035506, Stolarsky array *)
%t A387351 W[n_, k_] := Fibonacci[k + 1]  Floor[n*GoldenRatio] + (n - 1)  Fibonacci[k];
%t A387351 tw = Table[W[n, k], {n, 1, z}, {k, 1, z}];   (* A035513, Wythoff array *)
%t A387351 diff = tw - ts;
%t A387351 u = Table[diff[[n]][[2]], {n, 1, z}]
%t A387351 Flatten[Position[u, 0]]   (* A387349 *)
%t A387351 Flatten[Position[u, 1]]   (* A387350 *)
%t A387351 Flatten[Position[u, -1]]  (* A387351 *)
%Y A387351 Cf. A387348, A387349, A387350.
%K A387351 nonn,new
%O A387351 1,1
%A A387351 _Clark Kimberling_, Aug 27 2025