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A387350 Positions of 1's in A387348.

%I A387350 #5 Sep 01 2025 22:08:24
%S A387350 2,5,10,13,15,18,23,26,28,31,34,36,39,44,47,49,52,57,60,65,68,70,73,
%T A387350 78,81,83,86,89,91,94,99,102,104,107,112,115,120,123,125,128,133,136,
%U A387350 138,141,146,149,154,157,159,162,167,170,172,175,178,180,183,188
%N A387350 Positions of 1's in A387348.
%C A387350 This sequence together with A387349 and A387351 partition the positive integers.
%C A387350 Conjecture: the difference sequence, (3, 5, 3, 2, 3, 5, 3, 2, 3, 3, 2, 3, 5, 3, 2, 3, 5, 3, 5, ... ) has exactly 3 distinct terms.
%t A387350 z = 300;
%t A387350 A[n_, k_] := Module[{t, a, b}, t = (1 + Sqrt[5])/2;
%t A387350 a = Floor[n*(t + 1) + 1 + t/2]; b = Round[a*t]; ({b, a} . MatrixPower[{{1, 1}, {1, 0}}, k])[[2]]];
%t A387350 ts = Table[A[n, k], {n, 0, z - 1}, {k, 0, z - 1}];  (* A035506, Stolarsky array *)
%t A387350 W[n_, k_] := Fibonacci[k + 1]  Floor[n*GoldenRatio] + (n - 1)  Fibonacci[k];
%t A387350 tw = Table[W[n, k], {n, 1, z}, {k, 1, z}];   (* A035513, Wythoff array *)
%t A387350 diff = tw - ts;
%t A387350 u = Table[diff[[n]][[2]], {n, 1, z}]
%t A387350 Flatten[Position[u, 0]]   (* A387349 *)
%t A387350 Flatten[Position[u, 1]]   (* A387350 *)
%t A387350 Flatten[Position[u, -1]]  (* A387351 *)
%Y A387350 Cf. A387348, A387349, A387351.
%K A387350 nonn,new
%O A387350 1,1
%A A387350 _Clark Kimberling_, Aug 27 2025