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

1,2

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).

Links

Table of n, a(n) for n=1..78.

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

Example

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, ...
...

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}]]

Crossrefs

Cf. A106108, A132199, A137613.

Sequence in context: A050432 A343747 A334925 * A030346 A030336 A321650

Adjacent sequences: A247087 A247088 A247089 * A247091 A247092 A247093

Keyword

nonn,tabl

Author

L. Edson Jeffery, Nov 18 2014

Status

approved