A360379 a(n) = number of the antidiagonal of the Wythoff array (A035513) that includes prime(n).

2, 3, 4, 3, 4, 6, 7, 8, 7, 6, 9, 8, 11, 17, 7, 21, 23, 24, 26, 13, 10, 14, 21, 10, 10, 39, 40, 13, 27, 19, 49, 12, 53, 23, 17, 37, 11, 63, 41, 14, 69, 29, 12, 47, 76, 10, 81, 35, 55, 88, 12, 92, 18, 26, 40, 101, 65, 104, 67, 108, 44, 30, 118, 75, 120, 22

Offset: 1

Author

Clark Kimberling, Feb 05 2023

Keywords

• nonn
• easy

Comments

Conjecture: Only a finite number of positive integers are missing.

Examples

			The first 6 antidiagonals of the Wythoff array are (1), (2,4), (3,7,6), (5,11,10,9), (8,18,16,15,12), (12,29,26,24,20,14). The 10th prime is 29, which occurs in antidiagonal 6, so a(10) = 6.
		

Crossrefs

Cf. A000040, A035513, A332938, A360376, A360377, A360378, A360380.

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, Prime[#]]]] > 1 &]][[2]][[1]]]]
(* Peter J. C. Moses, Feb 08 2023 *)