login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A147696 Triangle read by rows: numbers n and columns k such that T(n, k) is n mod k. 0
0, 1, 0, 1, 1, 2, 0, 0, 1, 1, 0, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 0, 0, 0, 1, 1, 1, 0, 2, 2, 1, 0, 3, 0, 1, 0, 1, 1, 2, 1, 2, 0, 0, 2, 3, 1, 1, 3, 4, 0, 2, 0, 0, 1, 0, 1, 1, 0, 1, 2, 2, 1, 2, 3, 3, 0, 0, 0, 4, 1, 1, 1, 0, 1, 0, 2, 2, 1, 2, 1, 0, 3, 2, 3, 0, 1, 0, 3, 4, 1, 2, 1, 4, 5, 0, 0, 2, 0, 0, 1, 1, 3, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,6

COMMENTS

The triangle begins with (2, 2).

Each row can be produced from the previous row by adding one to each number and resetting to zero any which would equal their column number. A number p > 2 is prime iff row p contains no zeros.

A new column k begins at row n when n is a perfect square. T(n, k) is then 1, while T(n, sqrt(n) = k - 1) is 0.

Zeros correspond to ones in the Redheffer matrix. Various interesting patterns exist. For example, as noted above, T(n^2, n) = 0. Also:

T(n^2 + n, n) = T(n^2 + n, n + 1) = 0

T(n^2 + n - 2, n - 1) = 0

T(n^2 - 1, n - 1) = 0

For all k in some [0, c]:

T(n^2, 2 + k) = 0 if n is even

T(n^2, 2 + k) = 1 if n is odd

T(n^2 + n, 2 + k) = 0

Every zero is located on some parabola directed toward n = 0, having either even width and produced by an even sequence; or having an odd width and produced by an odd sequence. In either case, the relevant sequence has constant first differences 2. T(n^2, n) begins an odd parabola, while T(n^2 + n, n) begins an even parabola and parabolas of either variety extend from infinitely many other locations.

The triangle begins:

0

1

0 1

1 2

0 0

1 1

0 2

1 0 1

0 1 2

1 2 3

0 0 0

1 1 1

0 2 2

1 0 3

0 1 0 1

1 2 1 2

0 0 2 3

1 1 3 4

0 2 0 0

1 0 1 1

0 1 2 2

1 2 3 3

0 0 0 4

LINKS

Table of n, a(n) for n=2..105.

Eric Weisstein's World of Mathematics, Redheffer Matrix

CROSSREFS

Cf. A002321, A083058, A144912

Sequence in context: A323069 A325334 A280287 * A001842 A216654 A326016

Adjacent sequences:  A147693 A147694 A147695 * A147697 A147698 A147699

KEYWORD

easy,nonn,tabf

AUTHOR

Reikku Kulon, Nov 10 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 17 19:39 EDT 2021. Contains 343988 sequences. (Running on oeis4.)