A265345 -id:A265345 - cp's OEIS frontend

A265331 One-based row index to A265345.

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

Antti Karttunen, Dec 18 2015

Antti Karttunen, Table of n, a(n) for n = 1..19683

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.

(definec (A265331 n) (if (odd? n) 1 (+ 1 (A265331 (A265352 (/ n 2))))))

a(n) = A001511(A263273(n)).

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

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)).

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

Antti Karttunen, Dec 18 2015

Antti Karttunen, Table of n, a(n) for n = 1..6561
Indranil Ghosh, Python program to generate the sequence

One less than A265911.

Cf. A265345, A265352, A265354 (compare the scatter-plot).

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

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: A265345.

Cf. A265331, A265911.

(define (A265346 n) (let ((col (A265911 n)) (row (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 = A265911(n), and r = A265331(n).

A265347 Transpose of square array A265345.

Original entry on oeis.org

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

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 row are either all divisible by 3, or none of them are.
Sequence A265345 is the main entry for this idea, please see further comment there.

			The top left corner of the array:
   1,  2,  4,   8,  16, 64,    32,  184,  352,   704,  1408, ...
   3,  6, 12,  24,  48, 192,   96,  552, 1056,  2112,  4224, ...
   7, 10, 20,  40,  80, 160,  640,  320, 1600,  3520,  6080, ...
   5, 22, 28,  56, 112, 224,  448, 1720,  824,  4936,  9856, ...
   9, 18, 36,  72, 144, 576,  288, 1656, 3168,  6336, 12672, ...
  21, 30, 60, 120, 240, 480, 1920,  960, 4800, 10560, 18240, ...
  13, 26, 52, 208, 104, 520, 1144, 2072, 3712, 16120,  6968, ...
  19, 14, 76, 136, 200, 256,  512, 1024, 6040,  3992, 15424, ...
  25, 46, 68,  88, 496, 344, 1984, 1376, 5344,  7768, 15224, ...
  11, 58, 44, 232, 424, 608,  736, 4384, 2936, 17536, 11744, ...
  ...

Inverse permutation: A265348.

Transpose: A265345.

(define (A265347 n) (A265345bi (A025581 (+ -1 n)) (A002262 (+ -1 n)))) ;; o=1. Transpose of A265345.

A265895 Square array: A(row,col) = A263273(A265345(row,col)) = 2^row * A263273(A265341(col)).

Original entry on oeis.org

1, 3, 2, 5, 6, 4, 7, 10, 12, 8, 9, 14, 20, 24, 16, 15, 18, 28, 40, 48, 32, 13, 30, 36, 56, 80, 96, 64, 11, 26, 60, 72, 112, 160, 192, 128, 17, 22, 52, 120, 144, 224, 320, 384, 256, 19, 34, 44, 104, 240, 288, 448, 640, 768, 512, 21, 38, 68, 88, 208, 480, 576, 896, 1280, 1536, 1024, 39, 42, 76, 136, 176, 416, 960, 1152, 1792, 2560, 3072, 2048

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), ...

Shares with arrays A135764, A253551 and A254053 the property that odd terms are on the top row and when going downward in each column, terms grow by doubling.

			The top left corner of the array:
    1,   3,    5,    7,    9,   15,   13,   11,   17,   19,   21,   39,
    2,   6,   10,   14,   18,   30,   26,   22,   34,   38,   42,   78,
    4,  12,   20,   28,   36,   60,   52,   44,   68,   76,   84,  156,
    8,  24,   40,   56,   72,  120,  104,   88,  136,  152,  168,  312,
   16,  48,   80,  112,  144,  240,  208,  176,  272,  304,  336,  624,
   32,  96,  160,  224,  288,  480,  416,  352,  544,  608,  672, 1248,
   64, 192,  320,  448,  576,  960,  832,  704, 1088, 1216, 1344, 2496,
  128, 384,  640,  896, 1152, 1920, 1664, 1408, 2176, 2432, 2688, 4992,
  256, 768, 1280, 1792, 2304, 3840, 3328, 2816, 4352, 4864, 5376, 9984,
...

Inverse permutation: A265896.
The top row: 1+(2*A263273(n)).
Cf. A263273, A265341, A265345.
Differs from A135764 for the first time at n=16, where a(16) = 15, while A135764(16) = 11.

A(row,col) = A263273(A265345(row,col)).

A(row,col) = 2^row * A263273(A265341(col)).

A265341 Permutation of odd numbers: a(n) = 1 + (2*A265353(n)).

Original entry on oeis.org

1, 3, 7, 5, 9, 21, 13, 19, 25, 11, 15, 39, 17, 27, 63, 49, 57, 75, 31, 23, 67, 37, 55, 61, 43, 73, 79, 29, 33, 93, 47, 51, 147, 139, 111, 129, 35, 45, 117, 53, 81, 189, 157, 171, 225, 103, 69, 201, 145, 165, 183, 151, 219, 237, 85, 65, 193, 41, 71, 211, 121, 199, 205, 91, 59, 175, 109, 163, 169, 115, 181, 187, 97

Offset: 0

Antti Karttunen, Dec 07 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 0..9841

Topmost row of A265345.
Cf. A265353.
Cf. also A265342, A263273.

(define (A265341 n) (+ 1 (* 2 (A265353 n))))

a(n) = 1 + (2*A265353(n)).

A264980 Base-3 reversal of 2^n: a(n) = A030102(A000079(n)).

Original entry on oeis.org

1, 2, 4, 8, 16, 64, 32, 184, 352, 704, 1408, 1880, 2824, 14032, 10328, 56128, 100576, 145784, 189472, 370304, 731752, 4388248, 2924096, 11175712, 15965704, 31930448, 63861880, 383165344, 255439712, 1021772344, 510875648, 2550188248, 5619691648, 9689861048, 17830350904, 79068724264, 34109913224, 192259976368, 133338241880

Offset: 0

Antti Karttunen, Dec 05 2015

			2^5 = 32 in base 3 = "1012" (= A007089(32)) as 1*27 + 1*3 + 2*1 = 32. 2^6 = 64 in base 3 = "2101" as 2*27 + 1*9 + 1*1 = 64. "1012" reversed is "2101" and vice versa, thus a(5) = 64 and a(6) = 32.

Antti Karttunen, Table of n, a(n) for n = 0..512

Leftmost column of A265345.
Cf. A000079, A007089, A030102, A263273, A265210, A265342.
Cf. also A036215.

base(n) = {my(a=[n%3]); while(0Altug Alkan, Dec 29 2015

a(n) = A030102(A000079(n)) = A263273(A000079(n)).

a(0) = 1, for n >= 1, a(n) = A265342(a(n-1)).

cp's OEIS Frontend

A265331 One-based row index to A265345.

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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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A265910 Zero-based column index to array A265345.

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A265346 Inverse permutation to A265345.

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A265347 Transpose of square array A265345.

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A265895 Square array: A(row,col) = A263273(A265345(row,col)) = 2^row * A263273(A265341(col)).

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A265341 Permutation of odd numbers: a(n) = 1 + (2*A265353(n)).

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A264980 Base-3 reversal of 2^n: a(n) = A030102(A000079(n)).

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