A333087 Array (p(n,k)) read by antidiagonals: p(n,k) is the index of the prime in position (n,k) in the array A333086.

1, 2, 4, 3, 5, 9, 6, 10, 12, 7, 24, 15, 25, 21, 8, 51, 46, 37, 43, 11, 13, 251, 98, 271, 140, 32, 28, 20, 3121, 329, 1430, 35505, 231, 40, 93, 22, 42613, 500, 5185, 85968, 349, 130, 311, 151, 35

Offset: 1

Author

Clark Kimberling, Mar 10 2020

Keywords

• nonn
• tabl
• hard

Comments

As a sequence, this is a permutation of the positive integers.

Examples

			Northwest corner:
   1   2   3    6    24     51
   4   5  10   15    46     98
   9  12  25   37   271   1430
   7  21  43  140 35505  85968
   8  11  32  231   349   4410
  13  28  40  130  5655  20908
The 4th prime is 7, which occurs in the position (2,1) in A333086, so that p(2,1) = 4.
		

Crossrefs

Cf. A000040, A099000 (row 1), A333028, A333086.

Programs

Mathematica

W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];
t = Table[GCD[W[n, 1], W[n, 2]], {n, 1, 100}];
u = Flatten[Position[t, 1]] ; v[n_, k_] := W[u[[n]], k];
p[n_] := Table[v[n, k], {k, 1, 40}];
TableForm[Table[Select[p[n], PrimeQ], {n, 1, 10}]]
t1 = Table[PrimePi[Select[p[n], PrimeQ]], {n, 1, 10}]
tt[n_, k_] := t1[[n]][[k]];
Table[tt[n, k], {n, 1, 10}, {k, 1, 10}]  (* A333087 array *)
ttt = Table[tt[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten  (* A333087 sequence *)