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A278505 Square array constructed from Flavius sieve: Each row n (n >= 1) starts with A000960(n), followed by all numbers removed at the stage n of the sieve.

%I A278505 #19 Jun 23 2020 14:54:24
%S A278505 1,2,3,4,5,7,6,11,9,13,8,17,21,15,19,10,23,33,37,25,27,12,29,45,55,51,
%T A278505 31,39,14,35,57,75,85,73,43,49,16,41,69,97,111,121,99,61,63,18,47,81,
%U A278505 115,145,159,151,127,67,79,20,53,93,135,171,199,211,193,163,87,91,22,59,105,157,205,243,267,271,247,187,103,109
%N A278505 Square array constructed from Flavius sieve: Each row n (n >= 1) starts with A000960(n), followed by all numbers removed at the stage n of the sieve.
%C A278505 The array A(row,col) is read by descending antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
%H A278505 Antti Karttunen, <a href="/A278505/b278505.txt">Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of the array</a>
%H A278505 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H A278505 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%H A278505 <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%F A278505 A(row,1) = A000960(row); for col > 1, A(row,col) = A278507(row,col-1).
%F A278505 For all n >= 1, A(A278538(n), A278539(n)) = n.
%e A278505 The top left corner of the array:
%e A278505    1,  2,   4,   6,   8,  10,  12,  14,  16,  18
%e A278505    3,  5,  11,  17,  23,  29,  35,  41,  47,  53
%e A278505    7,  9,  21,  33,  45,  57,  69,  81,  93, 105
%e A278505   13, 15,  37,  55,  75,  97, 115, 135, 157, 175
%e A278505   19, 25,  51,  85, 111, 145, 171, 205, 231, 265
%e A278505   27, 31,  73, 121, 159, 199, 243, 283, 327, 367
%e A278505   39, 43,  99, 151, 211, 267, 319, 379, 433, 487
%e A278505   49, 61, 127, 193, 271, 343, 421, 483, 559, 631
%e A278505   63, 67, 163, 247, 339, 427, 519, 607, 691, 793
%e A278505   79, 87, 187, 303, 403, 523, 639, 739, 853, 963
%o A278505 (Scheme)
%o A278505 (define (A278505 n) (A278505bi (A002260 n) (A004736 n)))
%o A278505 (define (A278505bi row col) (if (= 1 col) (A000960 row) (A278507bi row (- col 1)))) ;; Code for A278507bi given in A278507.
%Y A278505 Inverse: A278506.
%Y A278505 Transpose: A278503.
%Y A278505 Column 1: A000960, column 2: A100287 (apart from its initial 1), A099259 (differences).
%Y A278505 Cf. A278538 (row index of n), A278539 (column index of n).
%Y A278505 Cf. also arrays A278507 and A278511 (different variants).
%Y A278505 Cf. also A255545 (an analogous array constructed for Lucky sieve).
%K A278505 nonn,tabl
%O A278505 1,2
%A A278505 _Antti Karttunen_, Nov 23 2016