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

1,2

Comments

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

Links

Table of n, a(n) for n=1..45.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A306779 A349947 A351652 * A091451 A365389 A246161

Adjacent sequences: A333084 A333085 A333086 * A333088 A333089 A333090

Keyword

nonn,tabl,hard

Author

Clark Kimberling, Mar 10 2020

Status

approved