A257514 -id:A257514 - cp's OEIS frontend

A257513 Square array A(row,col) = A083221(row+1,col) - A083221(row,col): the first differences of each column of array constructed from the sieve of Eratosthenes.

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

Offset: 1

Antti Karttunen, May 01 2015

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), ...

			The top left corner of the array:
1,   5,   9,  13,  17,  21,  25,  29,  33,  37,  41,  45,  49,  53,  57,  61
2,  16,  20,  34,  38,  52,  56,  70,  74,  88,  92, 106, 110, 124, 128, 142
2,  24,  42,  36,  54,  48,  66,  88,  92, 114, 132, 126, 144, 138, 156, 178
4,  72,  66,  96,  90, 120, 158, 138, 190, 192, 186, 216, 254, 306, 300, 324
2,  48,  78,  60,  90, 124,  84, 140, 126, 108, 138, 172, 184, 144, 200, 186
4, 120, 102, 144, 194, 150, 226, 216, 198, 240, 290, 314, 270, 346, 336, 318
2,  72, 114, 160,  96, 176, 150, 120, 162, 208, 220, 156, 236, 210, 180, 260
4, 168, 230, 162, 262, 240, 210, 264, 326, 350, 282, 382, 360, 330, 430, 408
6, 312, 232, 360, 338, 304, 374, 456, 492, 412, 540, 518, 484, 612, 590, 672
2, 120, 248, 198, 144, 210, 280, 292, 180, 308, 258, 204, 332, 282, 352, 426
6, 408, 370, 320, 406, 504, 540, 428, 588, 550, 500, 660, 622, 720, 830, 730
4, 312, 246, 336, 434, 458, 318, 490, 432, 366, 538, 480, 578, 684, 552, 486
2, 168, 258, 352, 364, 204, 380, 306, 228, 404, 330, 424, 522, 366, 288, 378
4, 360, 470, 494, 330, 526, 456, 378, 574, 504, 614, 732, 576, 498, 600, 522
6, 600, 636, 460, 684, 614, 532, 756, 686, 816, 958, 794, 712, 830, 748, 866
...

Transpose: A257514.
Row 1: A016813.
Column 1: A001223, Column 2: A069482, Column 3: A109805, Column 4: A226502 (apart from the first term).
Cf. A083221, A257251.

(define (A257513 n) (A257513bi (A002260 n) (A004736 n)))
(define (A257513bi row col) (- (A083221bi (+ 1 row) col) (A083221bi row col))) ;; A083221bi given in A083221.

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

A276609 Transpose of square array A276610.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Sep 13 2016

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

See A276610.

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

Transpose: A276610.

Cf. also A257514.

(define (A276609 n) (A276610bi (A004736 n) (A002260 n))) ;; Code for A276610bi given in A276610.

cp's OEIS Frontend

A257513 Square array A(row,col) = A083221(row+1,col) - A083221(row,col): the first differences of each column of array constructed from the sieve of Eratosthenes.

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