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A255127
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Ludic array: square array A(row,col), where row n lists the numbers removed at stage n in the sieve which produces Ludic numbers. Array is read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
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48
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2, 4, 3, 6, 9, 5, 8, 15, 19, 7, 10, 21, 35, 31, 11, 12, 27, 49, 59, 55, 13, 14, 33, 65, 85, 103, 73, 17, 16, 39, 79, 113, 151, 133, 101, 23, 18, 45, 95, 137, 203, 197, 187, 145, 25, 20, 51, 109, 163, 251, 263, 281, 271, 167, 29, 22, 57, 125, 191, 299, 325, 367, 403, 311, 205, 37, 24, 63, 139, 217, 343, 385, 461, 523, 457, 371, 253, 41
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OFFSET
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2,1
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COMMENTS
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The starting offset of the sequence giving the terms of square array is 2. However, we can tacitly assume that a(1) = 1 when the sequence is used as a permutation of natural numbers. However, term 1 itself is out of the array.
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LINKS
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EXAMPLE
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The top left corner of the array:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26
3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75
5, 19, 35, 49, 65, 79, 95, 109, 125, 139, 155, 169, 185
7, 31, 59, 85, 113, 137, 163, 191, 217, 241, 269, 295, 323
11, 55, 103, 151, 203, 251, 299, 343, 391, 443, 491, 539, 587
13, 73, 133, 197, 263, 325, 385, 449, 511, 571, 641, 701, 761
17, 101, 187, 281, 367, 461, 547, 629, 721, 809, 901, 989, 1079
23, 145, 271, 403, 523, 655, 781, 911, 1037, 1157, 1289, 1417, 1543
25, 167, 311, 457, 599, 745, 883, 1033, 1181, 1321, 1469, 1615, 1753
29, 205, 371, 551, 719, 895, 1073, 1243, 1421, 1591, 1771, 1945, 2117
...
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MATHEMATICA
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rows = 12; cols = 12; t = Range[2, 3000]; r = {1}; n = 1; While[n <= rows, k = First[t]; AppendTo[r, k]; t0 = t; t = Drop[t, {1, -1, k}]; ro[n++] = Complement[t0, t][[1 ;; cols]]]; A = Array[ro, rows]; Table[ A[[n - k + 1, k]], {n, 1, rows}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Mar 14 2016, after Ray Chandler *)
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PROG
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(Scheme)
(define (A255127bi row col) ((rowfun_n_for_A255127 row) col))
;; definec-macro memoizes its results:
(definec (rowfun_n_for_A255127 n) (if (= 1 n) (lambda (n) (+ n n)) (let* ((rowfun_for_remaining (rowfun_n_for_remaining_numbers (- n 1))) (eka (rowfun_for_remaining 0))) (COMPOSE rowfun_for_remaining (lambda (n) (* eka (- n 1)))))))
(definec (rowfun_n_for_remaining_numbers n) (if (= 1 n) (lambda (n) (+ n n 3)) (let* ((rowfun_for_prevrow (rowfun_n_for_remaining_numbers (- n 1))) (off (rowfun_for_prevrow 0))) (COMPOSE rowfun_for_prevrow (lambda (n) (+ 1 n (floor->exact (/ n (- off 1)))))))))
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CROSSREFS
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Inverse: A255128. (When considered as a permutation of natural numbers with a(1) = 1).
Cf. A260738 (index of the row where n occurs), A260739 (of the column).
A192607 gives all the numbers right of the leftmost column, and A192506 gives the composites among them.
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KEYWORD
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AUTHOR
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STATUS
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approved
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