A360485 a(n) = index of the antidiagonal of the Wythoff array (A035513) that includes n.

1, 2, 3, 2, 4, 3, 3, 5, 4, 4, 4, 5, 6, 6, 5, 5, 7, 5, 8, 6, 7, 9, 7, 6, 10, 6, 11, 8, 6, 12, 9, 7, 13, 8, 14, 10, 8, 15, 7, 16, 11, 7, 17, 12, 9, 18, 7, 19, 13, 10, 20, 8, 21, 14, 9, 22, 15, 11, 23, 9, 24, 16, 8, 25, 17, 12, 26, 8, 27, 18, 13, 28, 10, 29, 19

Offset: 1

Author

Clark Kimberling, Feb 09 2023

Keywords

• nonn
• easy

Comments

Each m appears exactly m times.

Crossrefs

Cf. A035513, A191360, A360379.

Programs

Mathematica

W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];
t = Table[W[n - k + 1, k], {n, 300}, {k, n, 1, -1}];
Map[#[[1]] &, Most[Reap[NestWhileList[# + 1 &, 1,
Length[Sow[FirstPosition[t, #]]] > 1 &]][[2]][[1]]]]
(* Peter J. C. Moses, Feb 08 2023 *)