A387349 Positions of 0's in A387348.

1, 4, 6, 7, 9, 11, 12, 14, 17, 19, 20, 22, 25, 27, 30, 32, 33, 35, 38, 40, 41, 43, 46, 48, 51, 53, 54, 56, 59, 61, 62, 64, 66, 67, 69, 72, 74, 75, 77, 80, 82, 85, 87, 88, 90, 93, 95, 96, 98, 100, 101, 103, 106, 108, 109, 111, 114, 116, 117, 119, 121, 122

Offset: 1

Author

Clark Kimberling, Aug 27 2025

Keywords

• nonn
• new

Comments

This sequence together with A387350 and A387351 partition the positive integers. Conjecture: the difference sequence (3, 2, 1, 2, 2, 1, 2, 3, 2, 1, 2, 3, 2, 3, 2, 1, ... ) has exactly 3 distinct terms.

Crossrefs

Cf. A387348, A387350, A387351.

Programs

Mathematica

z = 300;
A[n_, k_] := Module[{t, a, b}, t = (1 + Sqrt[5])/2;
a = Floor[n*(t + 1) + 1 + t/2]; b = Round[a*t]; ({b, a} . MatrixPower[{{1, 1}, {1, 0}}, k])[[2]]];
ts = Table[A[n, k], {n, 0, z - 1}, {k, 0, z - 1}];  (* A035506, Stolarsky array *)
W[n_, k_] := Fibonacci[k + 1]  Floor[n*GoldenRatio] + (n - 1)  Fibonacci[k];
tw = Table[W[n, k], {n, 1, z}, {k, 1, z}];   (* A035513, Wythoff array *)
diff = tw - ts;
u = Table[diff[[n]][[2]], {n, 1, z}]
Flatten[Position[u, 0]]   (* A387349 *)
Flatten[Position[u, 1]]   (* A387350 *)
Flatten[Position[u, -1]]  (* A387351 *)