A360379 - OEIS

%I #12 Aug 27 2023 16:54:01

%S 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,

%T 13,27,19,49,12,53,23,17,37,11,63,41,14,69,29,12,47,76,10,81,35,55,88,

%U 12,92,18,26,40,101,65,104,67,108,44,30,118,75,120,22

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

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

%e 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.

%t W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];

%t t = Table[W[n - k + 1, k], {n, 300}, {k, n, 1, -1}];

%t Map[#[[1]] &, Most[Reap[NestWhileList[# + 1 &, 1,

%t Length[Sow[FirstPosition[t, Prime[#]]]] > 1 &]][[2]][[1]]]]

%t (* _Peter J. C. Moses_, Feb 08 2023 *)

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

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Feb 05 2023