A283681 Unique sequence with a(1)=1, a(2)=2, representing an array read by antidiagonals in which the i-th row is this sequence itself multiplied by i.

1, 2, 2, 2, 4, 3, 2, 4, 6, 4, 4, 4, 6, 8, 5, 3, 8, 6, 8, 10, 6, 2, 6, 12, 8, 10, 12, 7, 4, 4, 9, 16, 10, 12, 14, 8, 6, 8, 6, 12, 20, 12, 14, 16, 9, 4, 12, 12, 8, 15, 24, 14, 16, 18, 10, 4, 8, 18, 16, 10, 18, 28, 16, 18, 20, 11, 4, 8, 12, 24, 20, 12, 21, 32, 18, 20, 22, 12, 6, 8

Offset

1,2

Comments

Any integer greater than 1 appears infinitely many times.

In particular, any n appears at the position (n^2 + n)/2. For prime n > 2, this is its first appearance; for composite n, it is not the first.

2 appears at the positions 2, 3, 4, 7, 22, 232, 26797, ... (A007501(n) + 1).

When the sequence is considered as an array, any prime n appears only in the first row (infinitely many times) and in the first column (once).

Links

Ivan Neretin, Table of n, a(n) for n = 1..26796

Formula

a((n^2+n)/2)=n.

Example

The sequence begins: 1, 2, 2, 2, 4, 3, 2, 4, 6, 4, ...
It represents a rectangular array read by downward antidiagonals. The first row of the array is this very sequence itself. The second row is this sequence multiplied by 2, and so on:
  1  2  2  2  4  3 ...
  2  4  4  4  8  ...
  3  6  6  6  ...
  4  8  8  ...
  5 10  ...
  6 ...
  ...

Mathematica

Nest[Flatten@Table[#[[n - i]]*i, {n, Length[#] + 1}, {i, n - 1}] &, {1, 2}, 4]

Crossrefs

Cf. A007501 (number of terms produced by the Mathematica code after n iterations).

Cf. A283682, A283683.

Sequence in context: A054709 A121806 A056944 * A222819 A194319 A208609

Adjacent sequences: A283678 A283679 A283680 * A283682 A283683 A283684

Keyword

nonn,tabl,nice,look

Author

Ivan Neretin, Mar 14 2017

Status

approved