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

1,1

Comments

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

Links

Table of n, a(n) for n=1..66.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A349049 A221356 A177329 * A253852 A103672 A309255

Adjacent sequences: A360376 A360377 A360378 * A360380 A360381 A360382

Keyword

nonn,easy

Author

Clark Kimberling, Feb 05 2023

Status

approved