login
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.
5

%I #13 Apr 28 2017 22:36:18

%S 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,

%T 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,

%U 16,10,18,28,16,18,20,11,4,8,12,24,20,12,21,32,18,20,22,12,6,8

%N 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.

%C Any integer greater than 1 appears infinitely many times.

%C 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.

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

%C 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).

%H Ivan Neretin, <a href="/A283681/b283681.txt">Table of n, a(n) for n = 1..26796</a>

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

%e The sequence begins: 1, 2, 2, 2, 4, 3, 2, 4, 6, 4, ...

%e 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:

%e 1 2 2 2 4 3 ...

%e 2 4 4 4 8 ...

%e 3 6 6 6 ...

%e 4 8 8 ...

%e 5 10 ...

%e 6 ...

%e ...

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

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

%Y Cf. A283682, A283683.

%K nonn,tabl,nice,look

%O 1,2

%A _Ivan Neretin_, Mar 14 2017