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

1,2

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), ...

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

Formula

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

Example

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
...

Prog

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

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.

Sequence in context: A065282 A274930 A080379 * A276849 A367210 A375613

Adjacent sequences: A257510 A257511 A257512 * A257514 A257515 A257516

Keyword

nonn,tabl,look

Author

Antti Karttunen, May 01 2015

Status

approved