A255545 Lucky / Unlucky array: Each row starts with n-th lucky number, followed by all unlucky numbers removed at stage n of the sieve.

1, 2, 3, 4, 5, 7, 6, 11, 19, 9, 8, 17, 39, 27, 13, 10, 23, 61, 57, 45, 15, 12, 29, 81, 91, 97, 55, 21, 14, 35, 103, 121, 147, 117, 85, 25, 16, 41, 123, 153, 199, 181, 177, 109, 31, 18, 47, 145, 183, 253, 243, 277, 225, 139, 33, 20, 53, 165, 217, 301, 315, 369, 345, 295, 157, 37, 22, 59, 187, 247, 351, 379, 471, 465, 447, 325, 175, 43

Offset: 1

Author

Antti Karttunen, Feb 25 2015

Keywords

• nonn
• tabl

Comments

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

Examples

			The top left corner of the array:
   1,   2,   4,   6,   8,  10,  12,   14,   16,   18,   20,   22,   24,   26,   28
   3,   5,  11,  17,  23,  29,  35,   41,   47,   53,   59,   65,   71,   77,   83
   7,  19,  39,  61,  81, 103, 123,  145,  165,  187,  207,  229,  249,  271,  291
   9,  27,  57,  91, 121, 153, 183,  217,  247,  279,  309,  343,  373,  405,  435
  13,  45,  97, 147, 199, 253, 301,  351,  403,  453,  507,  555,  609,  661,  709
  15,  55, 117, 181, 243, 315, 379,  441,  505,  571,  633,  697,  759,  825,  889
  21,  85, 177, 277, 369, 471, 567,  663,  757,  853,  949, 1045, 1141, 1239, 1333
  25, 109, 225, 345, 465, 589, 705,  829,  945, 1063, 1185, 1305, 1423, 1549, 1669
  31, 139, 295, 447, 603, 765, 913, 1075, 1227, 1377, 1537, 1689, 1843, 1999, 2155
  33, 157, 325, 493, 667, 835, 999, 1177, 1347, 1513, 1687, 1861, 2029, 2205, 2367
...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..5995; the first 109 antidiagonals of the array, flattened
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A255546.

Transpose: A255547.

Column 1: A000959. Other columns of array as in A255543, e.g. column 2: A219178.

Row 1: A004275 (starting from 1).

See A255551 for a slightly different variant.

Programs

Scheme

(define (A255545 n) (A255545bi (A002260 n) (A004736 n)))
(define (A255545bi row col) (if (= 1 col) (A000959 row) (A255543bi row (- col 1))))
;; Other code as in A255543.

Formula

For col = 1, A(row,col) = A000959(row); otherwise, A(row,col) = A255543(row,col-1).