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.]

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

Views

Author

Antti Karttunen, Dec 18 2015

Keywords

Examples

			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.

Links

Crossrefs

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.

Formula

a(n) = A007814(A263273(n)).
a(2n+1) = 0, a(2n) = 1 + 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).

A280509 a(n) = A051064(A246200(n)); 3-adic valuation of A057889(3*n).

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jan 09 2017

Keywords

Links

Crossrefs

Cf. A007949, A057889, A246200, A280508.
Differs from A051064 for the first time at n=23, where a(23) = 4, while A051064(23) = 1.
Cf. also A265331.

Programs

Formula

a(n) = A007949(A057889(3*n)).
a(n) = A051064(A246200(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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