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.

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

Offset

1,1

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

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

Example

The top left corner of the array:
     2,   2,   2,   2,   2,   2,   2,   2,   2,   2,   2,   2,   2,   2,   2
     6,   6,   6,   6,   6,   6,   6,   6,   6,   6,   6,   6,   6,   6,   6
    20,  10,  20,  10,  20,  10,  20,  10,  20,  10,  20,  10,  20,  10,  20
    42,  28,  14,  28,  14,  28,  42,  14,  42,  28,  14,  28,  14,  28,  42
   110,  22,  44,  22,  44,  66,  22,  66,  44,  22,  44,  66,  66,  22,  66
   156,  52,  26,  52,  78,  26,  78,  52,  26,  52,  78,  78,  26,  78,  52
   272,  34,  68, 102,  34, 102,  68,  34,  68, 102, 102,  34, 102,  68,  34
   342,  76, 114,  38, 114,  76,  38,  76, 114, 114,  38, 114,  76,  38, 114
   506, 138,  46, 138,  92,  46,  92, 138, 138,  46, 138,  92,  46, 138,  92
   812,  58, 174, 116,  58, 116, 174, 174,  58, 174, 116,  58, 174, 116, 174
   930, 186, 124,  62, 124, 186, 186,  62, 186, 124,  62, 186, 124, 186, 248
  1332, 148,  74, 148, 222, 222,  74, 222, 148,  74, 222, 148, 222, 296, 148
  1640,  82, 164, 246, 246,  82, 246, 164,  82, 246, 164, 246, 328, 164,  82
  1806, 172, 258, 258,  86, 258, 172,  86, 258, 172, 258, 344, 172,  86, 172
  2162, 282, 282,  94, 282, 188,  94, 282, 188, 282, 376, 188,  94, 188,  94
  2756, 318, 106, 318, 212, 106, 318, 212, 318, 424, 212, 106, 212, 106, 212
  ...

Mathematica

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;
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 *)

Prog

(Scheme)
(define (A257251 n) (A257251bi (A002260 n) (A004736 n)))
(define (A257251bi row col) (- (A083221bi row (+ 1 col)) (A083221bi row col))) ;; Code for A083221bi given in A083221.

Crossrefs

Transpose: A257252.

Column 1: A036689.

Row 4: 7 * A145011.

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

Cf. arrays A257255 and A257257, also A257513.

Sequence in context: A187564 A138061 A257257 * A068555 A167556 A221438

Adjacent sequences: A257248 A257249 A257250 * A257252 A257253 A257254

Keyword

nonn,tabl,look

Author

Antti Karttunen, Apr 19 2015

Status

approved