A255543 Unlucky array: Row n consists of unlucky numbers removed at the stage n of Lucky sieve.

2, 4, 5, 6, 11, 19, 8, 17, 39, 27, 10, 23, 61, 57, 45, 12, 29, 81, 91, 97, 55, 14, 35, 103, 121, 147, 117, 85, 16, 41, 123, 153, 199, 181, 177, 109, 18, 47, 145, 183, 253, 243, 277, 225, 139, 20, 53, 165, 217, 301, 315, 369, 345, 295, 157, 22, 59, 187, 247, 351, 379, 471, 465, 447, 325, 175, 24, 65, 207, 279, 403, 441, 567, 589, 603, 493, 381, 213

Offset

1,1

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), ...

Links

Antti Karttunen, Table of n, a(n) for n = 1..5886; the first 108 antidiagonals of the array, flattened

Example

Top left corner of the square array:
    2,   4,   6,   8,  10,  12,   14,   16,   18,   20,  22,    24,   26,   28,   30
    5,  11,  17,  23,  29,  35,   41,   47,   53,   59,  65,    71,   77,   83,   89
   19,  39,  61,  81, 103, 123,  145,  165,  187,  207, 229,   249,  271,  291,  313
   27,  57,  91, 121, 153, 183,  217,  247,  279,  309, 343,   373,  405,  435,  469
   45,  97, 147, 199, 253, 301,  351,  403,  453,  507, 555,   609,  661,  709,  763
   55, 117, 181, 243, 315, 379,  441,  505,  571,  633, 697,   759,  825,  889,  951
   85, 177, 277, 369, 471, 567,  663,  757,  853,  949, 1045, 1141, 1239, 1333, 1431
  109, 225, 345, 465, 589, 705,  829,  945, 1063, 1185, 1305, 1423, 1549, 1669, 1789
  139, 295, 447, 603, 765, 913, 1075, 1227, 1377, 1537, 1689, 1843, 1999, 2155, 2313
  157, 325, 493, 667, 835, 999, 1177, 1347, 1513, 1687, 1861, 2029, 2205, 2367, 2535
...

Mathematica

rows = cols = 12; L = 2 Range[0, 2000] + 1; A = Join[{2 Range[cols]}, Reap[For[n = 2, n <= rows, r = L[[n++]]; L0 = L; L = ReplacePart[L, Table[r i -> Nothing, {i, 1, Length[L]/r}]]; Sow[Complement[L0, L][[1 ;; cols]]]]][[2, 1]]]; Table[A[[n - k + 1, k]], {n, 1, Min[rows, cols]}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Mar 15 2016 *)

Prog

(Scheme)
(define (A255543 n) (A255543bi (A002260 n) (A004736 n)))
(define (A255543bi row col) ((rowfun_n_for_A255543 row) col))
;; Uses the memoizing definec-macro:
(definec (rowfun_n_for_A255543 n) (if (= 1 n) (lambda (n) (+ n n)) (let* ((rowfun_for_remaining (rowfun_n_for_A000959sieve (- n 1))) (eka (A000959 n))) (compose rowfun_for_remaining (lambda (n) (* eka n))))))
(definec (rowfun_n_for_A000959sieve n) (if (= 1 n) A005408shifted (let* ((prevrowfun (rowfun_n_for_A000959sieve (- n 1))) (everynth (prevrowfun n))) (compose-funs prevrowfun (nonzero-pos 1 1 (lambda (i) (modulo i everynth)))))))
(definec (A000959 n) ((rowfun_n_for_A000959sieve n) n))
(define (A005408shifted n) (- (* 2 n) 1))

Crossrefs

Permutation of A050505.

Row 1: A005843 (after zero), Row 2: A016969.

Column 1: A219178.

Main diagonal: A255549. The first subdiagonal: A255550 (apart from the initial term).

Transpose: A255544.

This is array A255545 without its leftmost column, A000959.

Cf. also arrays A255127 and A255551.

Sequence in context: A194607 A194637 A194600 * A256458 A376702 A276001

Adjacent sequences: A255540 A255541 A255542 * A255544 A255545 A255546

Keyword

nonn,tabl

Author

Antti Karttunen, Feb 25 2015

Status

approved