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A108760 Irregular array: n-th row consists of nonnegative integers i less than n such that n divides i(i+1).

%I A108760 #14 Mar 19 2022 09:21:52
%S A108760 0,1,0,2,0,3,0,4,0,2,3,5,0,6,0,7,0,8,0,4,5,9,0,10,0,3,8,11,0,12,0,6,7,
%T A108760 13,0,5,9,14,0,15,0,16,0,8,9,17,0,18,0,4,15,19,0,6,14,20,0,10,11,21,0,
%U A108760 22,0,8,15,23,0,24,0,12,13,25,0,26,0,7,20,27,0,28,0,5,9,14,15,20,24,29
%N A108760 Irregular array: n-th row consists of nonnegative integers i less than n such that n divides i(i+1).
%C A108760 Row n starts with 0 and ends with n-1.
%C A108760 Row n of this irregular array can be viewed as the first row of an infinite matrix with elements a_{j,i} = T(n,i)+n*j. That matrix consists of all nonnegative integers i such that n divides i(i+1).
%C A108760 I use these matrices to generate subsequences of A012132, as you may see on page 9 of my referenced work.
%H A108760 Robert Phillips, <a href="https://web.archive.org/web/20060919055917/http://www.usca.edu/math/~mathdept/bobp/pdf/tnumbers.pdf">Triangular Numbers which are sums of two Triangular Numbers</a>
%e A108760 Row 12 is 0,3,8,11 which is the first row of the matrix:
%e A108760    0  3  8 11
%e A108760   12 15 20 23
%e A108760   24 27 32 35
%e A108760   ...
%e A108760 giving all nonnegative integers i such that 12 divides i(i+1) (cf. A108752).
%e A108760 Array begins:
%e A108760   0, 1;
%e A108760   0, 2;
%e A108760   0, 3;
%e A108760   0, 4;
%e A108760   0, 2, 3, 5;
%e A108760   0, 6;
%e A108760   0, 7;
%e A108760   0, 8;
%e A108760   0, 4, 5, 9;
%e A108760   ...
%o A108760 (Python)
%o A108760 [i for n in range(2, 30) for i in range(0, n) if i*(i+1)%n==0] # _Andrey Zabolotskiy_, Mar 19 2022
%Y A108760 Cf. A012132, A108752.
%K A108760 nonn,easy,tabf
%O A108760 2,4
%A A108760 Robert Phillips (bobp(AT)usca.edu), Jun 24 2005
%E A108760 Edited by _Andrey Zabolotskiy_, Mar 19 2022