A253551 Square array: A(row,col) = 2^(row-1) * 1+(2*A156552(col)) = A156552(A246278(row,col)), read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

1, 3, 2, 5, 6, 4, 7, 10, 12, 8, 9, 14, 20, 24, 16, 11, 18, 28, 40, 48, 32, 17, 22, 36, 56, 80, 96, 64, 15, 34, 44, 72, 112, 160, 192, 128, 13, 30, 68, 88, 144, 224, 320, 384, 256, 19, 26, 60, 136, 176, 288, 448, 640, 768, 512, 33, 38, 52, 120, 272, 352, 576, 896, 1280, 1536, 1024, 23, 66, 76, 104, 240, 544, 704, 1152, 1792, 2560, 3072, 2048, 65, 46

Offset: 1

Author

Antti Karttunen, Jan 03 2015

Keywords

• nonn
• tabl

Comments

Shares with A135764 the property that A001511(n) = k for all terms n on row k and when going downwards in each column, terms grow by doubling.

Examples

			The top left corner of the array:
   1,  3,  5,   7,   9, 11,  17,  15,  13,  19,  33,  23,  65,  35,  21,
   2,  6, 10,  14,  18, 22,  34,  30,  26,  38,  66,  46, 130,  70,  42,
   4, 12, 20,  28,  36, 44,  68,  60,  52,  76, 132,  92, 260, 140,  84,
   8, 24, 40,  56,  72, 88, 136, 120, 104, 152, 264, 184, 520, 280, 168,
  16, 48, 80, 112, 144,176, 272, 240, 208, 304, 528, 368,1040, 560, 336,
...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1275; the first 50 antidiagonals of the array
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A253552.

Cf. A000079, A001511, A002260, A005408, A004736, A005940, A005941, A156552, A246278.

Differs from A135764 for the first time at n=22, where a(22) = 17, while A135764(22) = 13.

Formula

A(row,col) = A156552(A246278(row,col)).

A(row,col) = A135764(row, A005941(col)). [Is otherwise the same array as A135764, but the column positions have been permuted by A005941.]

A(row,col) = 2^(row-1) * ((2*A005941(col)) - 1) = 2^(row-1) * A005408(A156552(col)). [The above expands to this.]

As a composition of other permutations:

a(n) = A156552(A246278(n+1)). [When all three sequences are interpreted as one-dimensional sequences.]