cp's OEIS Frontend

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.

%I A283681 #13 Apr 28 2017 22:36:18
%S A283681 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 A283681 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 A283681 16,10,18,28,16,18,20,11,4,8,12,24,20,12,21,32,18,20,22,12,6,8
%N 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.
%C A283681 Any integer greater than 1 appears infinitely many times.
%C A283681 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 A283681 2 appears at the positions 2, 3, 4, 7, 22, 232, 26797, ... (A007501(n) + 1).
%C A283681 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 A283681 Ivan Neretin, <a href="/A283681/b283681.txt">Table of n, a(n) for n = 1..26796</a>
%F A283681 a((n^2+n)/2)=n.
%e A283681 The sequence begins: 1, 2, 2, 2, 4, 3, 2, 4, 6, 4, ...
%e A283681 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 A283681   1  2  2  2  4  3 ...
%e A283681   2  4  4  4  8  ...
%e A283681   3  6  6  6  ...
%e A283681   4  8  8  ...
%e A283681   5 10  ...
%e A283681   6 ...
%e A283681   ...
%t A283681 Nest[Flatten@Table[#[[n - i]]*i, {n, Length[#] + 1}, {i, n - 1}] &, {1, 2}, 4]
%Y A283681 Cf. A007501 (number of terms produced by the Mathematica code after n iterations).
%Y A283681 Cf. A283682, A283683.
%K A283681 nonn,tabl,nice,look
%O A283681 1,2
%A A283681 _Ivan Neretin_, Mar 14 2017