A051126 Table T(n,k) = n mod k read by antidiagonals (n >= 1, k >= 1).

0, 1, 0, 1, 0, 0, 1, 2, 1, 0, 1, 2, 0, 0, 0, 1, 2, 3, 1, 1, 0, 1, 2, 3, 0, 2, 0, 0, 1, 2, 3, 4, 1, 0, 1, 0, 1, 2, 3, 4, 0, 2, 1, 0, 0, 1, 2, 3, 4, 5, 1, 3, 2, 1, 0, 1, 2, 3, 4, 5, 0, 2, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 1, 3, 1, 1, 1, 0, 1, 2, 3, 4, 5, 6, 0, 2, 4, 2, 2, 0, 0, 1, 2, 3, 4, 5, 6, 7, 1, 3, 0, 3, 0, 1, 0

Offset

1,8

Links

Table of n, a(n) for n=1..105.

Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

Formula

As a linear array, the sequence is a(n) = A002260(n) mod A004736 (n) or a(n) = (n-(t*(t+1)/2)) mod ((t*t+3*t+4)/2-n), where t = floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Dec 19 2012

Example

Table begins in row n=1:
0  1  1  1  1  1  1  1  1  1 ...
0  0  2  2  2  2  2  2  2  2 ...
0  1  0  3  3  3  3  3  3  3 ...
0  0  1  0  4  4  4  4  4  4 ...
0  1  2  1  0  5  5  5  5  5 ...
0  0  0  2  1  0  6  6  6  6 ...
0  1  1  3  2  1  0  7  7  7 ...
0  0  2  0  3  2  1  0  8  8 ...
0  1  0  1  4  3  2  1  0  9 ...
0  0  1  2  0  4  3  2  1  0 ...
0  1  2  3  1  5  4  3  2  1 ...
0  0  0  0  2  0  5  4  3  2 ...
0  1  1  1  3  1  6  5  4  3 ...

Mathematica

TableForm[Table[Mod[n, k], {n, 1, 16}, {k, 1, 16}]] (* A051126 array *)
Table[Mod[n - k + 1, k], {n, 16}, {k, n, 1, -1}] // Flatten  (* A051126 sequence *)
(* Clark Kimberling, Feb 04 2016 *)

Crossrefs

Cf. A051127, A048158, A051777, A051778.

Sequence in context: A266825 A066438 A279291 * A168120 A355682 A063933

Adjacent sequences: A051123 A051124 A051125 * A051127 A051128 A051129

Keyword

nonn,tabl,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Dec 11 1999

Status

approved