A084287 Self-similar table, read by antidiagonals, where the k-th row is the product of the k-th prime with the antidiagonals of the first k rows of the table.

1, 2, 3, 4, 6, 5, 8, 9, 10, 7, 16, 12, 15, 14, 11, 32, 18, 20, 21, 22, 13, 64, 24, 30, 28, 33, 26, 17, 128, 27, 25, 42, 44, 39, 34, 19, 256, 48, 40, 35, 66, 52, 51, 38, 23, 512, 36, 45, 56, 55, 78, 68, 57, 46, 29, 1024, 96, 50, 63, 88, 65, 102, 76, 69, 58, 31, 2048, 54, 80, 70

Offset

1,2

Comments

A permutation of the natural numbers.

Links

Table of n, a(n) for n=1..70.

Example

1st row lists the powers of 2 in ascending order starting with 1;
2nd row = [3, 6, 9, 12, 18, 24, 27, 48, 36, 96, 54, 192, 72, 384, 81, ...] = 3*[1, 2, 3, 4, 6, 8, 9, 16, 12, 32, 18, 64, 24, 128, 27, ...];
3rd row = [5, 10, 15, 20, 30, 25, 40, 45, 50, 80, 60, 75, 160, 90, 100, ...] = 5*[1, 2, 3, 4, 6, 5, 8, 9, 10, 16, 12, 15, 32, 18, 20, ...];
4th row = [7, 14, 21, 28, 42, 35, 56, 63, 70, 49, 112, 84, 105, 98, ...] = 7*[1, 2, 3, 4, 6, 5, 8, 9, 10, 7, 16, 12, 15, 14, 32, 18, 20, 21, ...];
etc.
Table begins:
1,2,4,8,16,32,64,128,256,512,1024,2048,...
3,6,9,12,18,24,27,48,36,96,54,192,72,384,81,...
5,10,15,20,30,25,40,45,50,80,60,75,160,90,...
7,14,21,28,42,35,56,63,70,49,112,84,105,98,...
11,22,33,44,66,55,88,99,110,77,176,132,...
13,26,39,52,78,65,104,117,130,91,208,156,...
17,34,51,68,102,85,136,153,170,119,272,204,...
...

Crossrefs

Cf. A084288 (antidiagonal sums).

Sequence in context: A232559 A094138 A116538 * A263265 A263267 A257471

Adjacent sequences: A084284 A084285 A084286 * A084288 A084289 A084290

Keyword

tabl,nonn

Author

Paul D. Hanna, May 25 2003

Status

approved