A255543 - OEIS

%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