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A277820 Square array: A(r,1) = A065621(r); for c > 1, A(r,c) = A048724(A(r,c-1)), read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc. 12
1, 3, 2, 5, 6, 7, 15, 10, 9, 4, 17, 30, 27, 12, 13, 51, 34, 45, 20, 23, 14, 85, 102, 119, 60, 57, 18, 11, 255, 170, 153, 68, 75, 54, 29, 8, 257, 510, 427, 204, 221, 90, 39, 24, 25, 771, 514, 765, 340, 359, 238, 105, 40, 43, 26, 1285, 1542, 1799, 1020, 937, 306, 187, 120, 125, 46, 31, 3855, 2570, 2313, 1028, 1275, 854, 461, 136, 135, 114, 33, 28 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For all n >= 1, A277818 (= A268389(n)+1) gives the (one-based) index of the column where n is located in this array, while A268671(n) gives the (one-based) index of the row where it is on.

This array is obtained when one selects from A277320 the columns 1, 3, 5, 15, 17, 51, ..., i.e., those with an index A001317(k).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..3321; the first 81 antidiagonals of the array

Index entries for sequences related to binary expansion of n

Index entries for sequences that are permutations of the natural numbers

FORMULA

A(r,1) = A065621(r); for c > 1, A(r,c) = A048724(A(r,c-1)).

A(r,c) = A048675(A277810(r,c)).

As a composition of other permutations:

a(n) = A277901(A277880(n)).

EXAMPLE

The top left corner of the array:

   1,  3,   5,  15,  17,   51,   85,  255,   257,   771,  1285,  3855

   2,  6,  10,  30,  34,  102,  170,  510,   514,  1542,  2570,  7710

   7,  9,  27,  45, 119,  153,  427,  765,  1799,  2313,  6939, 11565

   4, 12,  20,  60,  68,  204,  340, 1020,  1028,  3084,  5140, 15420

  13, 23,  57,  75, 221,  359,  937, 1275,  3341,  5911, 14649, 19275

  14, 18,  54,  90, 238,  306,  854, 1530,  3598,  4626, 13878, 23130

  11, 29,  39, 105, 187,  461,  599, 1785,  2827,  7453, 10023, 26985

   8, 24,  40, 120, 136,  408,  680, 2040,  2056,  6168, 10280, 30840

  25, 43, 125, 135, 393,  667, 1965, 2295,  6425, 11051, 32125, 34695

  26, 46, 114, 150, 442,  718, 1874, 2550,  6682, 11822, 29298, 38550

  31, 33,  99, 165, 495,  561, 1619, 2805,  7967,  8481, 25443, 42405

  28, 36, 108, 180, 476,  612, 1708, 3060,  7196,  9252, 27756, 46260

  21, 63,  65, 195, 325,  975, 1105, 3315,  5397, 16191, 16705, 50115

  22, 58,  78, 210, 374,  922, 1198, 3570,  5654, 14906, 20046, 53970

  19, 53,  95, 225, 291,  869, 1455, 3825,  4883, 13621, 24415, 57825

  16, 48,  80, 240, 272,  816, 1360, 4080,  4112, 12336, 20560, 61680

  49, 83, 245, 287, 801, 1379, 4005, 4335, 12593, 21331, 62965, 73247

  50, 86, 250, 270, 786, 1334, 3930, 4590, 12850, 22102, 64250, 69390

  55, 89, 235, 317, 839, 1481, 3675, 4845, 14135, 22873, 60395, 80957

PROG

(Scheme)

(define (A277820 n) (A277820bi (A002260 n) (A004736 n)))

(define (A277820bi row col) (if (= 1 col) (A065621 row) (A048724 (A277820bi row (- col 1)))))

CROSSREFS

Inverse permutation: A277821.

Transpose: A277819.

Cf. A048724, A065621.

Row 1: A001317.

Column 1: A065621, column 2: A277823, column 3: A277825.

Cf. A268389, A277818, A268671.

Cf. also A193231, A277320, A277810, A276618 (A099884), A248513.

Other related tables or permutations: A277880, A277901.

Sequence in context: A257793 A083236 A302717 * A277680 A303764 A079973

Adjacent sequences:  A277817 A277818 A277819 * A277821 A277822 A277823

KEYWORD

nonn,tabl,base

AUTHOR

Antti Karttunen, Nov 01 2016

STATUS

approved

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Last modified February 26 05:51 EST 2020. Contains 332277 sequences. (Running on oeis4.)