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A360379
a(n) = number of the antidiagonal of the Wythoff array (A035513) that includes prime(n).
4
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.
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 *)
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 05 2023
STATUS
approved