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 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. 8

%I

%S 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,

%T 52,272,2,6,10,14,22,26,34,342,2,6,20,28,44,52,68,76,506,2,6,10,42,66,

%U 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

%N 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.

%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="/A257251/b257251.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,col+1) - A083221(row,col).

%F A(row,col) = 2*A257253(row,col).

%e The top left corner of the array:

%e 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

%e 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

%e 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20

%e 42, 28, 14, 28, 14, 28, 42, 14, 42, 28, 14, 28, 14, 28, 42

%e 110, 22, 44, 22, 44, 66, 22, 66, 44, 22, 44, 66, 66, 22, 66

%e 156, 52, 26, 52, 78, 26, 78, 52, 26, 52, 78, 78, 26, 78, 52

%e 272, 34, 68, 102, 34, 102, 68, 34, 68, 102, 102, 34, 102, 68, 34

%e 342, 76, 114, 38, 114, 76, 38, 76, 114, 114, 38, 114, 76, 38, 114

%e 506, 138, 46, 138, 92, 46, 92, 138, 138, 46, 138, 92, 46, 138, 92

%e 812, 58, 174, 116, 58, 116, 174, 174, 58, 174, 116, 58, 174, 116, 174

%e 930, 186, 124, 62, 124, 186, 186, 62, 186, 124, 62, 186, 124, 186, 248

%e 1332, 148, 74, 148, 222, 222, 74, 222, 148, 74, 222, 148, 222, 296, 148

%e 1640, 82, 164, 246, 246, 82, 246, 164, 82, 246, 164, 246, 328, 164, 82

%e 1806, 172, 258, 258, 86, 258, 172, 86, 258, 172, 258, 344, 172, 86, 172

%e 2162, 282, 282, 94, 282, 188, 94, 282, 188, 282, 376, 188, 94, 188, 94

%e 2756, 318, 106, 318, 212, 106, 318, 212, 318, 424, 212, 106, 212, 106, 212

%e ...

%t lim = 13; Clear[row]; row[n_] := row[n] = Take[Prime[n]*Select[Range[lim^2], GCD[#*Prime[n], Product[Prime[i], {i, n-1}]] == 1&], lim] // Differences;

%t A[n_, k_] := row[n][[k]]; Table[A[n-k+1, k], {n, 1, lim-1}, {k, n, 1, -1}] // Flatten (* _Jean-François Alcover_, Mar 08 2016, after _Michael De Vlieger_ in A083221 *)

%o (Scheme)

%o (define (A257251 n) (A257251bi (A002260 n) (A004736 n)))

%o (define (A257251bi row col) (- (A083221bi row (+ 1 col)) (A083221bi row col))) ;; Code for A083221bi given in A083221.

%Y Transpose: A257252.

%Y Column 1: A036689.

%Y Row 4: 7 * A145011.

%Y Cf. A083221, A257253 (same array but with terms divided by 2).

%Y Cf. arrays A257255 and A257257, also A257513.

%K nonn,tabl,look

%O 1,1

%A _Antti Karttunen_, Apr 19 2015

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Last modified September 23 15:06 EDT 2020. Contains 337310 sequences. (Running on oeis4.)