A254053 Square array: A(row,col) = 2^(row-1) * ((2*A249745(col))-1) = A064216(A254051(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, 11, 14, 20, 24, 16, 13, 22, 28, 40, 48, 32, 17, 26, 44, 56, 80, 96, 64, 19, 34, 52, 88, 112, 160, 192, 128, 9, 38, 68, 104, 176, 224, 320, 384, 256, 23, 18, 76, 136, 208, 352, 448, 640, 768, 512, 29, 46, 36, 152, 272, 416, 704, 896, 1280, 1536, 1024, 15, 58, 92, 72, 304, 544, 832, 1408, 1792, 2560, 3072, 2048, 31, 30

Offset

1,2

Comments

Shares with A135764 and A253551 the property that A001511(n) = k for all terms n on row k and when going downward in each column, terms grow by doubling.

Links

Antti Karttunen, Table of n, a(n) for n = 1..2080; the first 64 antidiagonals of the array

Index entries for sequences that are permutations of the natural numbers

Formula

A(row,col) = A135764(row, A249745(col)). [Is otherwise the same array as A135764, but the column positions have been permuted by A249745.]

A(row,col) = 2^(row-1) * ((2*A249745(col))-1) = 2^(row-1) * A254050(col). [The above expands to this.]

a(n) = A064989(A135765(n)).

As a composition of other permutations:

a(n) = A064216(A254051(n)). [As an array: A(row,col) = A064216(A254051(row,col)).]

Example

The top left corner of the array:
   1,  3,  5,   7,  11,  13,  17,  19,   9,  23,  29,  15,  31,  37,  41,  43,
   2,  6, 10,  14,  22,  26,  34,  38,  18,  46,  58,  30,  62,  74,  82,  86,
   4, 12, 20,  28,  44,  52,  68,  76,  36,  92, 116,  60, 124, 148, 164, 172,
   8, 24, 40,  56,  88, 104, 136, 152,  72, 184, 232, 120, 248, 296, 328, 344,
  16, 48, 80, 112, 176, 208, 272, 304, 144, 368, 464, 240, 496, 592, 656, 688,
...

Prog

(Scheme, several alternative versions)
(define (A254053 n) (A135764bi (A002260 n) (A249745 (A004736 n))))
(define (A254053 n) (* (A000079 (- (A002260 n) 1)) (+ -1 (* 2 (A249745 (A004736 n))))))
(define (A254053 n) (* (A000079 (- (A002260 n) 1)) (A254050 (A004736 n))))
(define (A254053bi row col) (A064216 (A254051bi row col)))
(define (A254053 n) (A254053bi (A002260 n) (A004736 n)))
(define (A254053 n) (A064216 (A254051 n)))

Crossrefs

Inverse: A254054.

Similar or related permutations: A135764, A253551, A064216, A254051.

Cf. A000079, A001511, A002260, A004736, A064989, A135765, A249745, A254049, A254050.

Sequence in context: A135764 A253551 A265895 * A360307 A303774 A303776

Adjacent sequences: A254050 A254051 A254052 * A254054 A254055 A254056

Keyword

nonn,tabl

Author

Antti Karttunen, Jan 24 2015

Status

approved