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

Author

Ivan Neretin, Mar 14 2017

Keywords

• nonn
• tabl
• nice
• look

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).

Examples

			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 ...
  ...
		

Links

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

Crossrefs

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

Cf. A283682, A283683.

Programs

Mathematica

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

Formula

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