|
%I #21 Mar 15 2016 05:10:30
%S 2,4,5,6,11,19,8,17,39,27,10,23,61,57,45,12,29,81,91,97,55,14,35,103,
%T 121,147,117,85,16,41,123,153,199,181,177,109,18,47,145,183,253,243,
%U 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
%N Unlucky array: Row n consists of unlucky numbers removed at the stage n of Lucky sieve.
%C 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), ...
%H Antti Karttunen, <a href="/A255543/b255543.txt">Table of n, a(n) for n = 1..5886; the first 108 antidiagonals of the array, flattened</a>
%e Top left corner of the square array:
%e 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
%e 5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89
%e 19, 39, 61, 81, 103, 123, 145, 165, 187, 207, 229, 249, 271, 291, 313
%e 27, 57, 91, 121, 153, 183, 217, 247, 279, 309, 343, 373, 405, 435, 469
%e 45, 97, 147, 199, 253, 301, 351, 403, 453, 507, 555, 609, 661, 709, 763
%e 55, 117, 181, 243, 315, 379, 441, 505, 571, 633, 697, 759, 825, 889, 951
%e 85, 177, 277, 369, 471, 567, 663, 757, 853, 949, 1045, 1141, 1239, 1333, 1431
%e 109, 225, 345, 465, 589, 705, 829, 945, 1063, 1185, 1305, 1423, 1549, 1669, 1789
%e 139, 295, 447, 603, 765, 913, 1075, 1227, 1377, 1537, 1689, 1843, 1999, 2155, 2313
%e 157, 325, 493, 667, 835, 999, 1177, 1347, 1513, 1687, 1861, 2029, 2205, 2367, 2535
%e ...
%t 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 *)
%o (Scheme)
%o (define (A255543 n) (A255543bi (A002260 n) (A004736 n)))
%o (define (A255543bi row col) ((rowfun_n_for_A255543 row) col))
%o ;; Uses the memoizing definec-macro:
%o (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))))))
%o (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)))))))
%o (definec (A000959 n) ((rowfun_n_for_A000959sieve n) n))
%o (define (A005408shifted n) (- (* 2 n) 1))
%Y Permutation of A050505.
%Y Row 1: A005843 (after zero), Row 2: A016969.
%Y Column 1: A219178.
%Y Main diagonal: A255549. The first subdiagonal: A255550 (apart from the initial term).
%Y Transpose: A255544.
%Y This is array A255545 without its leftmost column, A000959.
%Y Cf. also arrays A255127 and A255551.
%K nonn,tabl
%O 1,1
%A _Antti Karttunen_, Feb 25 2015
|
