A257255 -id:A257255 - cp's OEIS frontend

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

Antti Karttunen, Apr 19 2015

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), ...

			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
  ...

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.

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 *)

(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.

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

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

A257257 Square array A(row,col) = A255127(row,col+1) - A255127(row,col): the first differences of each row of Ludic array.

Original entry on oeis.org

2, 2, 6, 2, 6, 14, 2, 6, 16, 24, 2, 6, 14, 28, 44, 2, 6, 16, 26, 48, 60, 2, 6, 14, 28, 48, 60, 84, 2, 6, 16, 24, 52, 64, 86, 122, 2, 6, 14, 26, 48, 66, 94, 126, 142, 2, 6, 16, 28, 48, 62, 86, 132, 144, 176, 2, 6, 14, 26, 44, 60, 94, 120, 146, 166, 216, 2, 6, 16, 24, 48, 64, 86, 132, 142, 180, 234, 252

Offset: 1

Antti Karttunen, Apr 19 2015

The array A(row,col) is read by downwards antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

			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
   14,  16,  14,  16,  14,  16,  14,  16,  14,  16,  14,  16,  14,  16,  14
   24,  28,  26,  28,  24,  26,  28,  26,  24,  28,  26,  28,  24,  26,  28
   44,  48,  48,  52,  48,  48,  44,  48,  52,  48,  48,  48,  44,  52,  48
   60,  60,  64,  66,  62,  60,  64,  62,  60,  70,  60,  60,  62,  64,  60
   84,  86,  94,  86,  94,  86,  82,  92,  88,  92,  88,  90,  90,  84,  90
  122, 126, 132, 120, 132, 126, 130, 126, 120, 132, 128, 126, 130, 128, 126
  142, 144, 146, 142, 146, 138, 150, 148, 140, 148, 146, 138, 150, 138, 150
  176, 166, 180, 168, 176, 178, 170, 178, 170, 180, 174, 172, 176, 178, 176
  216, 234, 226, 242, 228, 226, 240, 218, 234, 246, 220, 230, 234, 226, 234
  252, 270, 254, 274, 258, 254, 258, 276, 262, 266, 258, 256, 264, 276, 264
  274, 284, 268, 284, 304, 270, 282, 278, 294, 282, 282, 276, 282, 288, 292
  308, 316, 314, 316, 320, 316, 312, 308, 324, 336, 316, 302, 316, 314, 322
  360, 360, 354, 368, 360, 372, 370, 368, 352, 360, 380, 354, 370, 380, 352
  412, 434, 424, 420, 426, 440, 426, 420, 432, 424, 422, 444, 424, 422, 430
  ...

Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of the array

Column 1: A256482.
Cf. A255127.
Cf. A257258 (same array but with terms divided by 2).
Cf. also arrays A257251 and A257255.

(define (A257257 n) (A257257bi (A002260 n) (A004736 n)))
(define (A257257bi row col) (- (A255127bi row (+ 1 col)) (A255127bi row col))) ;; Code for A255127bi given in A255127.

A(row,col) = A255127(row,col+1) - A255127(row,col).

A(row,col) = 2*A257258(row,col).

A257256 Difference between {the first unlucky number removed at the n-th stage of Lucky sieve} and {the n-th Lucky number}: a(n) = A219178(n) - A000959(n).

Original entry on oeis.org

1, 2, 12, 18, 32, 40, 64, 84, 108, 124, 138, 170, 206, 214, 274, 296, 318, 338, 348, 378, 426, 454, 498, 532, 564, 600, 662, 678, 710, 736, 766, 836, 874, 920, 944, 954, 1078, 1104, 1120, 1170, 1202, 1254, 1296, 1332, 1378, 1416, 1434, 1466, 1592, 1612, 1660, 1696, 1778, 1786, 1820, 1888, 1932, 1952, 2058

Offset: 1

Antti Karttunen, Apr 29 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..767

First column of A257255.

Cf. A000959, A219178.

(define (A257256 n) (- (A219178 n) (A000959 n)))

a(n) = A219178(n) - A000959(n).

cp's OEIS Frontend

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.

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A257257 Square array A(row,col) = A255127(row,col+1) - A255127(row,col): the first differences of each row of Ludic array.

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Scheme

Formula

A257256 Difference between {the first unlucky number removed at the n-th stage of Lucky sieve} and {the n-th Lucky number}: a(n) = A219178(n) - A000959(n).

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Scheme

Formula