2,3

This triangle is roughly twice the usual width. Odd rows and columns congruent to 2 modulo 3 are omitted; otherwise the triangle would begin like this:

2:..0...0...0

3:..0...2...0...2

4:..7...5...3...0...5

5:..0...0...0...0...2...0

6:.13..11...0...7...5...3..11

7:..0...0...0...0...0...0...0...0

8:.19..17...0..13..11...0...7...5..17

Every odd row afterward would then be entirely filled with zeros and every third column would contain zeros, often following an initial prime.

The triangle begins as follows:

b

--+b^2..+0..+1..+3..+4..+6..+7..+9.+10.+12

2.:......0...0

4.:......7...5...0...5

6.:.....13..11...7...5..11

8.:.....19..17..13..11...7...5

10:......0..23..19..17..13..11...7..23

12:.....31..29...0..23..19..17..13..11..29

Some diagonals are entirely filled with zeros; for example, the first such diagonal begins at b = 32 and there is another for b in [40, 42].

The fraction |A144912(b, b^2)| / b approaches 3 or nearly 3.

For n = b and m = b + 2, ((n, x) + (m, x)) / 2 approximates (m, x + 1) = (n, x - 1), where x is the index of a column disregarding k.

The units digit in columns follows the repeating sequence {1, 7, 3, 9, 5}, with nearly all fives omitted and occasional other omissions.

The units digit in rows follows the sequence {1, 9, 5, 3, 9, 7, 3, 1, 7, 5}.

The complete repeating unit is:

1 9 5 3 9 7 3 1 7 5

7 5 1 9 5 3 9 7 3 1

3 1 7 5 1 9 5 3 9 7

9 7 3 1 7 5 1 9 5 3

5 3 9 7 3 1 7 5 1 9

Cf. A144912

Sequence in context: A152627 A113223 A096414 this_sequence A096435 A021855 A145176

Adjacent sequences: A144920 A144921 A144922 this_sequence A144924 A144925 A144926

easy,nonn,tabf

Reikku Kulon (reikku(AT)gmail.com), Sep 25 2008