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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)).
10
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
1,2
COMMENTS
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)).
FORMULA
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.]
EXAMPLE
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, .
...
PROG
(Scheme)
(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.
CROSSREFS
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.
Sequence in context: A101307 A283997 A096899 * A340447 A360983 A154448
KEYWORD
nonn,tabl,base
AUTHOR
Antti Karttunen, Dec 18 2015
STATUS
approved