A265910 -id:A265910 - cp's OEIS frontend

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)).

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.]

A265911 One-based column index to array A265345.

Original entry on oeis.org

1, 1, 2, 1, 4, 2, 3, 1, 5, 3, 10, 2, 7, 8, 11, 1, 13, 5, 8, 3, 6, 4, 20, 2, 9, 7, 14, 4, 28, 6, 19, 1, 29, 20, 37, 5, 22, 23, 12, 3, 58, 17, 25, 10, 38, 9, 31, 2, 16, 26, 32, 7, 40, 14, 23, 4, 17, 10, 65, 6, 24, 19, 15, 1, 56, 11, 21, 9, 47, 13, 59, 5, 26, 22, 18, 8, 74, 12, 27, 3, 41

Offset: 1

Antti Karttunen, Dec 18 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10328

One more than A265910.

Cf. A265345.

Scheme
```
(define (A265911 n) (+ 1 (A265910 n)))
```

a(n) = 1 + A265910(n).

A265330 Zero-based row index to A265345; 2-adic valuation of bijective base-3 reversal of n: a(n) = A007814(A263273(n)).

Original entry on oeis.org

0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 6, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 3

Offset: 1

Antti Karttunen, Dec 18 2015

			For n = 32, in base-3 "1012" [= A007089(32)], when we reverse it, we get "2101" [= A007089(64)], and 2-adic valuation of 64 [= "1000000" = A007088(64)] is 6, thus a(32) = 6.

Antti Karttunen, Table of n, a(n) for n = 1..6561

One less than A265331.
Cf. A007088, A007089, A263273, A265345, A265352.
Cf. A265910 (corresponding other index).
Cf. also A265336, A265337, A265340.
Differs from A007814 for the first time at n=32, where a(32) = 6, while A007814(32) = 5.

a(n) = A007814(A263273(n)).

a(2n+1) = 0, a(2n) = 1 + a(A265352(n)).

cp's OEIS Frontend

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)).

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A265911 One-based column index to array A265345.

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A265330 Zero-based row index to A265345; 2-adic valuation of bijective base-3 reversal of n: a(n) = A007814(A263273(n)).

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