A277820 - OEIS

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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.

13

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 A376890 A302717 * A277680 A303764 A079973

Adjacent sequences: A277817 A277818 A277819 * A277821 A277822 A277823

KEYWORD

nonn,tabl,base

AUTHOR

Antti Karttunen, Nov 01 2016

STATUS

approved