A257513 - OEIS

%I #18 May 03 2015 17:55:41

%S 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,

%T 78,120,2,29,56,48,90,60,102,72,4,33,70,66,120,90,144,114,168,6,37,74,

%U 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

%N 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.

%C 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), ...

%H Antti Karttunen, <a href="/A257513/b257513.txt">Table of n, a(n) for n = 1..3321; the first 81 antidiagonals of the array</a>

%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>

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

%e The top left corner of the array:

%e 1,   5,   9,  13,  17,  21,  25,  29,  33,  37,  41,  45,  49,  53,  57,  61

%e 2,  16,  20,  34,  38,  52,  56,  70,  74,  88,  92, 106, 110, 124, 128, 142

%e 2,  24,  42,  36,  54,  48,  66,  88,  92, 114, 132, 126, 144, 138, 156, 178

%e 4,  72,  66,  96,  90, 120, 158, 138, 190, 192, 186, 216, 254, 306, 300, 324

%e 2,  48,  78,  60,  90, 124,  84, 140, 126, 108, 138, 172, 184, 144, 200, 186

%e 4, 120, 102, 144, 194, 150, 226, 216, 198, 240, 290, 314, 270, 346, 336, 318

%e 2,  72, 114, 160,  96, 176, 150, 120, 162, 208, 220, 156, 236, 210, 180, 260

%e 4, 168, 230, 162, 262, 240, 210, 264, 326, 350, 282, 382, 360, 330, 430, 408

%e 6, 312, 232, 360, 338, 304, 374, 456, 492, 412, 540, 518, 484, 612, 590, 672

%e 2, 120, 248, 198, 144, 210, 280, 292, 180, 308, 258, 204, 332, 282, 352, 426

%e 6, 408, 370, 320, 406, 504, 540, 428, 588, 550, 500, 660, 622, 720, 830, 730

%e 4, 312, 246, 336, 434, 458, 318, 490, 432, 366, 538, 480, 578, 684, 552, 486

%e 2, 168, 258, 352, 364, 204, 380, 306, 228, 404, 330, 424, 522, 366, 288, 378

%e 4, 360, 470, 494, 330, 526, 456, 378, 574, 504, 614, 732, 576, 498, 600, 522

%e 6, 600, 636, 460, 684, 614, 532, 756, 686, 816, 958, 794, 712, 830, 748, 866

%e ...

%o (Scheme)

%o (define (A257513 n) (A257513bi (A002260 n) (A004736 n)))

%o (define (A257513bi row col) (- (A083221bi (+ 1 row) col) (A083221bi row col))) ;; A083221bi given in A083221.

%Y Transpose: A257514.

%Y Row 1: A016813.

%Y Column 1: A001223, Column 2: A069482, Column 3: A109805, Column 4: A226502 (apart from the first term).

%Y Cf. A083221, A257251.

%K nonn,tabl,look

%O 1,2

%A _Antti Karttunen_, May 01 2015