A333086 Array read by antidiagonals: row n consists of the primes in row n of the array A333028.

2, 3, 7, 5, 11, 23, 13, 29, 37, 17, 89, 47, 97, 73, 19, 233, 199, 157, 191, 31, 41, 1597, 521, 1741, 809, 131, 107, 71, 28657, 2207, 11933, 421493, 1453, 173, 487, 79, 514229, 3571, 50549, 1103483, 2351, 733, 2063, 877, 149, 433494437, 9349, 214129, 1785473

Offset: 1

Author

Clark Kimberling, Mar 10 2020

Keywords

• nonn
• tabl
• hard

Comments

The array shows, in order, the primes in the Wythoff array after deletion of all nonprimes. Every prime occurs exactly once; that is, every prime is uniquely expressible as F(k+1)*floor(n*tau) + (n-1)F(k), where tau = golden ratio (A001622), F = A000045 (Fibonacci numbers), and n and k are positive integers. We assume as true the conjecture that each row is infinite.

Examples

			Northwest corner:
    2    3    5    13      89      233
    7   11   29    47     199      521
   23   37   97   157    1741    11933
   17   73  191   809  421493  1103483
   19   31  131  1453    2351    42187
   41  107  173   733   55717   236021
Row 22 begins with 30631, 2187696161008162875319987.
		

Crossrefs

Cf. A000040, A333028, A333087.

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, 200}];
u = Flatten[Position[t, 1]] ; v[n_, k_] := W[u[[n]], k];
p[n_] := Table[v[n, k], {k, 1, 1000}];
TableForm[Table[Select[p[n], PrimeQ], {n, 1, 100}]]