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%I #15 Feb 28 2015 14:49:23
%S 2,4,3,6,5,7,8,11,19,9,10,17,39,27,13,12,23,61,57,45,15,14,29,81,91,
%T 97,55,21,16,35,103,121,147,117,85,25,18,41,123,153,199,181,177,109,
%U 31,20,47,145,183,253,243,277,225,139,33,22,53,165,217,301,315,369,345,295,157,37,24,59,187,247,351,379,471,465,447,325,175,43
%N Lucky / Unlucky array, shifted version, read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
%C Note how in comparison to A255545, the even numbers on the first row have been shifted one step left, "pushing" term 1 out of the array proper. This was done to obtain a better alignment with arrays like A083221 and A255127 associated with other sieves, from which one may then induce permutations like A255553 by cross-referencing.
%C The starting offset of the sequence giving the terms in square array is 2. However, we can tacitly assume that a(1) = 1 when the sequence is used one-dimensionally as a permutation of natural numbers.
%H Antti Karttunen, <a href="/A255551/b255551.txt">Table of n, a(n) for n = 2..5996; the first 109 antidiagonals of the array, flattened</a>
%F For row = 1, A(row,col) = 2*col; For row > 1 and col = 1, A(row,col) = A000959(row); otherwise, A(row,col) = A255543(row,col-1).
%e The top left corner of the array:
%e 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
%e 3, 5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83
%e 7, 19, 39, 61, 81, 103, 123, 145, 165, 187, 207, 229, 249, 271, 291
%e 9, 27, 57, 91, 121, 153, 183, 217, 247, 279, 309, 343, 373, 405, 435
%e 13, 45, 97, 147, 199, 253, 301, 351, 403, 453, 507, 555, 609, 661, 709
%e 15, 55, 117, 181, 243, 315, 379, 441, 505, 571, 633, 697, 759, 825, 889
%e 21, 85, 177, 277, 369, 471, 567, 663, 757, 853, 949, 1045, 1141, 1239, 1333
%e 25, 109, 225, 345, 465, 589, 705, 829, 945, 1063, 1185, 1305, 1423, 1549, 1669
%e 31, 139, 295, 447, 603, 765, 913, 1075, 1227, 1377, 1537, 1689, 1843, 1999, 2155
%e 33, 157, 325, 493, 667, 835, 999, 1177, 1347, 1513, 1687, 1861, 2029, 2205, 2367
%e ...
%o (Scheme)
%o (define (A255551 n) (if (<= n 1) n (A255551bi (A002260 (- n 1)) (A004736 (- n 1)))))
%o (define (A255551bi row col) (cond ((= 1 row) (+ col col)) ((= 1 col) (A000959 row)) (else (A255543bi row (- col 1)))))
%o ;; Other code as in A255543.
%Y Inverse: A255552.
%Y Variant of array A255545. (See also A255543).
%Y Row 1: A005843 (even numbers).
%Y Column 1: 2 followed by A000959(2..) (Lucky numbers from their second term onward).
%Y Main diagonal: A255550.
%Y Similar arrays: A083221, A255127.
%Y Associated permutations: A255553, A255554.
%K nonn,tabl
%O 2,1
%A _Antti Karttunen_, Feb 26 2015
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