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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.

%I A333087 #6 Mar 10 2020 23:49:36
%S A333087 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,
%T A333087 32,28,20,3121,329,1430,35505,231,40,93,22,42613,500,5185,85968,349,
%U A333087 130,311,151,35
%N 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.
%C A333087 As a sequence, this is a permutation of the positive integers.
%e A333087 Northwest corner:
%e A333087    1   2   3    6    24     51
%e A333087    4   5  10   15    46     98
%e A333087    9  12  25   37   271   1430
%e A333087    7  21  43  140 35505  85968
%e A333087    8  11  32  231   349   4410
%e A333087   13  28  40  130  5655  20908
%e A333087 The 4th prime is 7, which occurs in the position (2,1) in A333086, so that p(2,1) = 4.
%t A333087 W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];
%t A333087 t = Table[GCD[W[n, 1], W[n, 2]], {n, 1, 100}];
%t A333087 u = Flatten[Position[t, 1]] ; v[n_, k_] := W[u[[n]], k];
%t A333087 p[n_] := Table[v[n, k], {k, 1, 40}];
%t A333087 TableForm[Table[Select[p[n], PrimeQ], {n, 1, 10}]]
%t A333087 t1 = Table[PrimePi[Select[p[n], PrimeQ]], {n, 1, 10}]
%t A333087 tt[n_, k_] := t1[[n]][[k]];
%t A333087 Table[tt[n, k], {n, 1, 10}, {k, 1, 10}]  (* A333087 array *)
%t A333087 ttt = Table[tt[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten  (* A333087 sequence *)
%Y A333087 Cf. A000040, A099000 (row 1), A333028, A333086.
%K A333087 nonn,tabl,hard
%O A333087 1,2
%A A333087 _Clark Kimberling_, Mar 10 2020