A265347 -id:A265347 - cp's OEIS frontend

A265348 Inverse permutation to A265347.

1, 2, 3, 4, 10, 5, 6, 7, 15, 9, 55, 8, 28, 44, 66, 11, 91, 20, 36, 13, 21, 14, 210, 12, 45, 35, 105, 19, 406, 27, 190, 22, 435, 230, 703, 26, 253, 299, 78, 18, 1711, 170, 325, 76, 741, 54, 496, 17, 136, 377, 528, 43, 820, 119, 276, 25, 153, 65, 2145, 34, 300, 209, 120, 16, 1596, 77, 231, 64, 1128, 104, 1770, 33, 351, 275, 171, 53, 2775, 90, 378, 24, 861

Offset: 1

Antti Karttunen, Dec 18 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10328
Index entries for sequences that are permutations of the natural numbers

Inverse: A265347.

Cf. A265331, A265911.

(define (A265348 n) (let ((row (A265911 n)) (col (A265331 n))) (* (/ 1 2) (- (expt (+ row col) 2) row col col col -2))))

a(n) = (1/2) * ((c+r)^2 - r - 3*c + 2), where c = A265331(n), and r = A265911(n).

A265345 Square array A(row,col): For row=0, A(0,col) = A265341(col), for row > 0, A(row,col) = A265342(A(row-1,col)).

Original entry on oeis.org

1, 3, 2, 7, 6, 4, 5, 10, 12, 8, 9, 22, 20, 24, 16, 21, 18, 28, 40, 48, 64, 13, 30, 36, 56, 80, 192, 32, 19, 26, 60, 72, 112, 160, 96, 184, 25, 14, 52, 120, 144, 224, 640, 552, 352, 11, 46, 76, 208, 240, 576, 448, 320, 1056, 704, 15, 58, 68, 136, 104, 480, 288, 1720, 1600, 2112, 1408

Offset: 1

Antti Karttunen, Dec 18 2015

Square array A(row,col) is read by downwards antidiagonals as: A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), A(0,3), A(1,2), A(2,1), A(3,0), ...
All the terms in the same column are either all divisible by 3, or none of them are.
Reducing A265342 to its constituent sequences gives A265342(n) = A263273(2*A263273(n)). Iterating this function k times starting from n reduces to (because A263273 is an involution, so pairs of them are canceled) to A263273((2^k)*A263273(n)).

			The top left corner of the array:
    1,    3,    7,    5,    9,   21,   13,   19,   25,   11,   15,    39, .
    2,    6,   10,   22,   18,   30,   26,   14,   46,   58,   66,    78, .
    4,   12,   20,   28,   36,   60,   52,   76,   68,   44,   84,   156, .
    8,   24,   40,   56,   72,  120,  208,  136,   88,  232,  168,   624, .
   16,   48,   80,  112,  144,  240,  104,  200,  496,  424,  336,   312, .
   64,  192,  160,  224,  576,  480,  520,  256,  344,  608,  672,  1560, .
   32,   96,  640,  448,  288, 1920, 1144,  512, 1984,  736, 1344,  3432, .
  184,  552,  320, 1720, 1656,  960, 2072, 1024, 1376, 4384, 5160,  6216, .
  352, 1056, 1600,  824, 3168, 4800, 3712, 6040, 5344, 2936, 2472, 11136, .
  ...

Inverse: A265346.
Transpose: A265347.
Leftmost column: A264980.
Topmost row: A265341.
Row index: A265330 (zero-based), A265331 (one-based).
Column index: A265910 (zero-based), A265911 (one-based).
Cf. also A265342.
Related permutations: A263273, A265895.

(define (A265345 n) (A265345bi (A002262 (+ -1 n)) (A025581 (+ -1 n)))) ;; o=1.
(define (A265345bi row col) (A263273 (* (A000079 row) (A263273 (A265341 col))))) ;; Faster than below.
(define (A265345bi row col) (if (= 0 row) (A265341 col) (A265342 (A265345bi (- row 1) col)))) ;; row>=0, col>=0.

For row=0, A(0,col) = A265341(col), for row>0, A(row,col) = A265342(A(row-1,col)).

A(row, col) = A263273((2^row) * A263273(A265341(col))). [The above reduces to this.]

cp's OEIS Frontend

A265348 Inverse permutation to A265347.

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