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

1,2

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.

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

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.]

Example

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,
...

Prog

(Scheme, four alternative definitions)
(define (A253551 n) (A156552 (A246278 (+ 1 n))))
(define (A253551 n) (A135764bi (A002260 n) (A005941 (A004736 n)))) ;; Code for A135764bi given in A135764.
(define (A253551 n) (* (A000079 (- (A002260 n) 1)) (+ -1 (* 2 (A005941 (A004736 n))))))
(define (A253551 n) (* (A000079 (- (A002260 n) 1)) (A005408 (A156552 (A004736 n)))))

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.

Sequence in context: A026098 A365232 A135764 * A265895 A254053 A360307

Adjacent sequences: A253548 A253549 A253550 * A253552 A253553 A253554

Keyword

nonn,tabl

Author

Antti Karttunen, Jan 03 2015

Status

approved