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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 1-3 of 3 results.

A257514 Transpose of square array A257513.

Original entry on oeis.org

1, 2, 5, 2, 16, 9, 4, 24, 20, 13, 2, 72, 42, 34, 17, 4, 48, 66, 36, 38, 21, 2, 120, 78, 96, 54, 52, 25, 4, 72, 102, 60, 90, 48, 56, 29, 6, 168, 114, 144, 90, 120, 66, 70, 33, 2, 312, 230, 160, 194, 124, 158, 88, 74, 37, 6, 120, 232, 162, 96, 150, 84, 138, 92, 88, 41, 4, 408, 248, 360, 262, 176, 226, 140, 190, 114, 92, 45
Offset: 1

Views

Author

Antti Karttunen, May 01 2015

Keywords

Comments

The array is read by downwards antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
See A257513.

Examples

			The top left corner of the array:
   1,   2,   2,   4,   2,   4,   2,   4,   6,   2,   6,   4,   2,   4,   6
   5,  16,  24,  72,  48, 120,  72, 168, 312, 120, 408, 312, 168, 360, 600
   9,  20,  42,  66,  78, 102, 114, 230, 232, 248, 370, 246, 258, 470, 636
  13,  34,  36,  96,  60, 144, 160, 162, 360, 198, 320, 336, 352, 494, 460
  17,  38,  54,  90,  90, 194,  96, 262, 338, 144, 406, 434, 364, 330, 684
  21,  52,  48, 120, 124, 150, 176, 240, 304, 210, 504, 458, 204, 526, 614
  25,  56,  66, 158,  84, 226, 150, 210, 374, 280, 540, 318, 380, 456, 532
  29,  70,  88, 138, 140, 216, 120, 264, 456, 292, 428, 490, 306, 378, 756
  33,  74,  92, 190, 126, 198, 162, 326, 492, 180, 588, 432, 228, 574, 686
  37,  88, 114, 192, 108, 240, 208, 350, 412, 308, 550, 366, 404, 504, 816
  41,  92, 132, 186, 138, 290, 220, 282, 540, 258, 500, 538, 330, 614, 958
  45, 106, 126, 216, 172, 314, 156, 382, 518, 204, 660, 480, 424, 732, 794
  49, 110, 144, 254, 184, 270, 236, 360, 484, 332, 622, 578, 522, 576, 712
  53, 124, 138, 306, 144, 346, 210, 330, 612, 282, 720, 684, 366, 498, 830
  57, 128, 156, 300, 200, 336, 180, 430, 590, 352, 830, 552, 288, 600, 748
  ...

Links

Crossrefs

Transpose of A257513.
Column 1: A016813.
Row 1: A001223, Row 2: A069482, Row 3: A109805, Row 4: A226502 (apart from the first term).
Cf. also A083140, A083221, A257252.

Programs

A257251 Square array A(row,col) = A083221(row,col+1) - A083221(row,col): the first differences of each row of array constructed from the sieve of Eratosthenes.

Original entry on oeis.org

2, 2, 6, 2, 6, 20, 2, 6, 10, 42, 2, 6, 20, 28, 110, 2, 6, 10, 14, 22, 156, 2, 6, 20, 28, 44, 52, 272, 2, 6, 10, 14, 22, 26, 34, 342, 2, 6, 20, 28, 44, 52, 68, 76, 506, 2, 6, 10, 42, 66, 78, 102, 114, 138, 812, 2, 6, 20, 14, 22, 26, 34, 38, 46, 58, 930, 2, 6, 10, 42, 66, 78, 102, 114, 138, 174, 186, 1332
Offset: 1

Views

Author

Antti Karttunen, Apr 19 2015

Keywords

Comments

The array is read by downwards antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

Examples

			The top left corner of the array:
     2,   2,   2,   2,   2,   2,   2,   2,   2,   2,   2,   2,   2,   2,   2
     6,   6,   6,   6,   6,   6,   6,   6,   6,   6,   6,   6,   6,   6,   6
    20,  10,  20,  10,  20,  10,  20,  10,  20,  10,  20,  10,  20,  10,  20
    42,  28,  14,  28,  14,  28,  42,  14,  42,  28,  14,  28,  14,  28,  42
   110,  22,  44,  22,  44,  66,  22,  66,  44,  22,  44,  66,  66,  22,  66
   156,  52,  26,  52,  78,  26,  78,  52,  26,  52,  78,  78,  26,  78,  52
   272,  34,  68, 102,  34, 102,  68,  34,  68, 102, 102,  34, 102,  68,  34
   342,  76, 114,  38, 114,  76,  38,  76, 114, 114,  38, 114,  76,  38, 114
   506, 138,  46, 138,  92,  46,  92, 138, 138,  46, 138,  92,  46, 138,  92
   812,  58, 174, 116,  58, 116, 174, 174,  58, 174, 116,  58, 174, 116, 174
   930, 186, 124,  62, 124, 186, 186,  62, 186, 124,  62, 186, 124, 186, 248
  1332, 148,  74, 148, 222, 222,  74, 222, 148,  74, 222, 148, 222, 296, 148
  1640,  82, 164, 246, 246,  82, 246, 164,  82, 246, 164, 246, 328, 164,  82
  1806, 172, 258, 258,  86, 258, 172,  86, 258, 172, 258, 344, 172,  86, 172
  2162, 282, 282,  94, 282, 188,  94, 282, 188, 282, 376, 188,  94, 188,  94
  2756, 318, 106, 318, 212, 106, 318, 212, 318, 424, 212, 106, 212, 106, 212
  ...

Links

Crossrefs

Transpose: A257252.
Column 1: A036689.
Row 4: 7 * A145011.
Cf. A083221, A257253 (same array but with terms divided by 2).
Cf. arrays A257255 and A257257, also A257513.

Programs

Formula

A(row,col) = A083221(row,col+1) - A083221(row,col).
A(row,col) = 2*A257253(row,col).

A276610 Square array A(row,col) = A255127(row+1,col) - A255127(row,col): the first differences of each column of Ludic array, read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

Original entry on oeis.org

1, 5, 2, 9, 10, 2, 13, 20, 12, 4, 17, 28, 24, 24, 2, 21, 38, 36, 44, 18, 4, 25, 46, 48, 66, 30, 28, 6, 29, 56, 58, 90, 46, 54, 44, 2, 33, 64, 68, 114, 60, 84, 84, 22, 4, 37, 74, 82, 136, 74, 104, 122, 40, 38, 8, 41, 82, 92, 152, 86, 136, 156, 54, 60, 48, 4, 45, 92, 102, 174, 106, 162, 194, 76, 94, 116, 40, 2
Offset: 1

Views

Author

Antti Karttunen, Sep 13 2016

Keywords

Comments

Not all rows are monotonic. See A276620 for their first differences.

Examples

			The top left 16 x 15 corner of the array:
1,  5,   9,  13,  17,  21,  25,  29,  33,  37,  41,  45,  49,  53,  57,  61
2, 10,  20,  28,  38,  46,  56,  64,  74,  82,  92, 100, 110, 118, 128, 136
2, 12,  24,  36,  48,  58,  68,  82,  92, 102, 114, 126, 138, 148, 158, 172
4, 24,  44,  66,  90, 114, 136, 152, 174, 202, 222, 244, 264, 284, 310, 330
2, 18,  30,  46,  60,  74,  86, 106, 120, 128, 150, 162, 174, 192, 204, 216
4, 28,  54,  84, 104, 136, 162, 180, 210, 238, 260, 288, 318, 346, 366, 396
6, 44,  84, 122, 156, 194, 234, 282, 316, 348, 388, 428, 464, 504, 548, 584
2, 22,  40,  54,  76,  90, 102, 122, 144, 164, 180, 198, 210, 230, 240, 264
4, 38,  60,  94, 120, 150, 190, 210, 240, 270, 302, 330, 364, 390, 430, 456
8, 48, 116, 162, 236, 288, 336, 406, 446, 510, 576, 622, 680, 738, 786, 844
4, 40,  76, 104, 136, 166, 194, 212, 270, 298, 318, 356, 382, 412, 462, 492
2, 24,  38,  52,  62, 108, 124, 148, 150, 182, 198, 222, 242, 260, 272, 300
4, 38,  70, 116, 148, 164, 210, 240, 270, 300, 354, 388, 414, 448, 474, 504
6, 58, 102, 142, 194, 234, 290, 348, 408, 436, 460, 524, 576, 630, 696, 726
8, 60, 134, 204, 256, 322, 390, 446, 498, 578, 642, 684, 774, 828, 870, 948

Links

Crossrefs

Transpose: A276609.
Row 1: A016813.
Column 1: A260723 (from the second 1 onward), Column 2: A276606.
Cf. A255127, A269379.
Cf. also arrays A257257, A257513 and A276620 (gives the first differences of each row).

Programs

Formula

A(row,col) = A255127(row+1,col) - A255127(row,col).
A(row,col) = A269379(A255127(row,col)) - A255127(row,col).
Showing 1-3 of 3 results.

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