A387350 Positions of 1's in A387348.

2, 5, 10, 13, 15, 18, 23, 26, 28, 31, 34, 36, 39, 44, 47, 49, 52, 57, 60, 65, 68, 70, 73, 78, 81, 83, 86, 89, 91, 94, 99, 102, 104, 107, 112, 115, 120, 123, 125, 128, 133, 136, 138, 141, 146, 149, 154, 157, 159, 162, 167, 170, 172, 175, 178, 180, 183, 188

Offset

1,1

Comments

This sequence together with A387349 and A387351 partition the positive integers.

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.

Links

Table of n, a(n) for n=1..58.

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 *)

Crossrefs

Cf. A387348, A387349, A387351.

Sequence in context: A192539 A046462 A188025 * A187949 A180161 A349243

Adjacent sequences: A387347 A387348 A387349 * A387351 A387352 A387353

Keyword

nonn

Author

Clark Kimberling, Aug 27 2025

Status

approved