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

Author

Antti Karttunen, May 01 2015

Keywords

• nonn
• tabl
• look

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:
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
...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..3321; the first 81 antidiagonals of the array
• Index entries for sequences generated by sieves

Crossrefs

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.

Programs

Scheme

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

Formula

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