A247090 Eric Rowland's generalization of A132199 as a rectangular array A read by upward antidiagonals.

1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 5, 3, 1, 1, 1, 1, 1, 1, 5, 3, 1, 1, 1, 1, 2, 1, 1, 5, 3, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

L. Edson Jeffery, Nov 18 2014

Keywords

• nonn
• tabl

Comments

Conjecture [Rowland] (paraphrased): Let A be the above array with entry A(n,k) in row n and column k. For each n, there exists an index N(n) >= 1 such that A(n,j) is either 1 or prime for all j > N(n).

Examples

			Array A begins:
1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 1,  1, ...
2, 1, 1, 1, 1, 1, 1, 1, 1,  1, 1,  1, ...
1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 1,  1, ...
2, 3, 1, 5, 3, 1, 1, 1, 1, 11, 3,  1, ...
1, 3, 1, 5, 3, 1, 1, 1, 1, 11, 3,  1, ...
2, 1, 1, 5, 3, 1, 1, 1, 1, 11, 3,  1, ...
1, 1, 1, 5, 3, 1, 1, 1, 1, 11, 3,  1, ...
2, 1, 1, 1, 1, 7, 1, 1, 1,  1, 1, 13, ...
1, 1, 1, 1, 1, 7, 1, 1, 1,  1, 1, 13, ...
2, 3, 1, 1, 1, 1, 1, 1, 1, 11, 3,  1, ...
1, 3, 1, 1, 1, 1, 1, 1, 1, 11, 3,  1, ...
2, 1, 1, 1, 1, 1, 1, 1, 1, 11, 3,  1, ...
...
		

Links

• Eric S. Rowland, A natural prime-generating recurrence, J. Integer Seq., 11 (2008), Article 08.2.8.

Crossrefs

Cf. A106108, A132199, A137613.

Programs

Mathematica

(* Array A: *)
max := 13; b[n_, 1] := n; b[n_, k_] := b[n, k] = b[n, k - 1] + GCD[k, b[n, k - 1]]; Grid[Transpose[Differences[Transpose[Table[b[n, k], {n, max}, {k, max}]]]]]
(* Array antidiagonals flattened: *)
max := 13; b[n_, 1] := n; b[n_, k_] := b[n, k] = b[n, k - 1] + GCD[k, b[n, k - 1]]; Flatten[Table[Transpose[Differences[Transpose[Table[b[n, k], {n, max}, {k, max}]]]][[n - k + 1]][[k]], {n, max - 1}, {k, n}]]