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A255127 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), ... 48
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

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.

LINKS

Antti Karttunen, Table of n, a(n) for n = 2..10441; the first 144 antidiagonals of array, flattened

EXAMPLE

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

...

MATHEMATICA

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-Fran├žois Alcover, Mar 14 2016, after Ray Chandler *)

PROG

(Scheme)

(define (A255127 n) (if (<= n 1) n (A255127bi (A002260 (- n 1)) (A004736 (- n 1)))))

(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)))))))))

CROSSREFS

Transpose: A255129.

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).

Main diagonal: A255410.

Column 1: A003309 (without the initial 1). Column 2: A254100.

Row 1: A005843, Row 2: A016945, Row 3: A255413, Row 4: A255414, Row 5: A255415, Row 6: A255416, Row 7: A255417, Row 8: A255418, Row 9: A255419.

A192607 gives all the numbers right of the leftmost column, and A192506 gives the composites among them.

Cf. A272565, A271419, A271420 and permutations A269379, A269380, A269384.

Cf. also related or derived arrays A260717, A257257, A257258 (first differences of rows), A276610 (of columns), A276580.

Analogous arrays for other sieves: A083221, A255551, A255543.

Sequence in context: A163280 A056537 A293054 * A083221 A246278 A246366

Adjacent sequences:  A255124 A255125 A255126 * A255128 A255129 A255130

KEYWORD

nonn,tabl,look

AUTHOR

Antti Karttunen, Feb 22 2015

STATUS

approved

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Last modified September 24 23:13 EDT 2020. Contains 337325 sequences. (Running on oeis4.)