cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

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

Views

Author

Antti Karttunen, Dec 18 2015

Keywords

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)).

Examples

			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, .
  ...

Links

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.

Programs

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.]

A265331 One-based row index to A265345.

Original entry on oeis.org

1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 7, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 6, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 7, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 4
Offset: 1

Views

Author

Antti Karttunen, Dec 18 2015

Keywords

Links

Crossrefs

One more than A265330.
Cf. A007088, A007089, A263273, A265345, A265352.
Cf. A265911 (corresponding other index).
Differs from A001511 for the first time at n=32, where a(32) = 7, while A001511(32) = 6.

Programs

Formula

a(n) = A001511(A263273(n)).
a(2n+1) = 1, a(2n) = 1 + a(A265352(n)).

A265910 Zero-based column index to array A265345.

Original entry on oeis.org

0, 0, 1, 0, 3, 1, 2, 0, 4, 2, 9, 1, 6, 7, 10, 0, 12, 4, 7, 2, 5, 3, 19, 1, 8, 6, 13, 3, 27, 5, 18, 0, 28, 19, 36, 4, 21, 22, 11, 2, 57, 16, 24, 9, 37, 8, 30, 1, 15, 25, 31, 6, 39, 13, 22, 3, 16, 9, 64, 5, 23, 18, 14, 0, 55, 10, 20, 8, 46, 12, 58, 4, 25, 21, 17, 7, 73, 11, 26, 2, 40
Offset: 1

Views

Author

Antti Karttunen, Dec 18 2015

Keywords

Links

Crossrefs

One less than A265911.
Cf. A265345, A265352, A265354 (compare the scatter-plot).

Formula

a(2n+1) = A265354(n), a(2n) = a(A265352(n)).

A265346 Inverse permutation to A265345.

Original entry on oeis.org

1, 3, 2, 6, 7, 5, 4, 10, 11, 8, 46, 9, 22, 38, 56, 15, 79, 17, 29, 13, 16, 12, 191, 14, 37, 30, 92, 18, 379, 23, 172, 28, 407, 212, 667, 24, 232, 278, 67, 19, 1654, 155, 301, 69, 704, 47, 466, 20, 121, 353, 497, 39, 781, 107, 254, 25, 137, 57, 2081, 31, 277, 192, 106, 21, 1541, 68, 211, 58, 1082, 93, 1712, 32, 326, 255, 154, 48, 2702, 80, 352, 26, 821
Offset: 1

Views

Author

Antti Karttunen, Dec 18 2015

Keywords

Links

Crossrefs

Inverse: A265345.
Cf. A265331, A265911.

Programs

  • Scheme
    (define (A265346 n) (let ((col (A265911 n)) (row (A265331 n))) (* (/ 1 2) (- (expt (+ row col) 2) row col col col -2))))

Formula

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

A265348 Inverse permutation to A265347.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Dec 18 2015

Keywords

Links

Crossrefs

Inverse: A265347.
Cf. A265331, A265911.

Programs

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

Formula

a(n) = (1/2) * ((c+r)^2 - r - 3*c + 2), where c = A265331(n), and r = A265911(n).
Showing 1-5 of 5 results.

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