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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.
9

%I #19 Jun 23 2020 14:54:24

%S 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 31,39,14,35,57,75,85,73,43,49,16,41,69,97,111,121,99,61,63,18,47,81,

%U 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 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 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 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 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>

%H <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>

%F A(row,1) = A000960(row); for col > 1, A(row,col) = A278507(row,col-1).

%F For all n >= 1, A(A278538(n), A278539(n)) = n.

%e The top left corner of the array:

%e 1, 2, 4, 6, 8, 10, 12, 14, 16, 18

%e 3, 5, 11, 17, 23, 29, 35, 41, 47, 53

%e 7, 9, 21, 33, 45, 57, 69, 81, 93, 105

%e 13, 15, 37, 55, 75, 97, 115, 135, 157, 175

%e 19, 25, 51, 85, 111, 145, 171, 205, 231, 265

%e 27, 31, 73, 121, 159, 199, 243, 283, 327, 367

%e 39, 43, 99, 151, 211, 267, 319, 379, 433, 487

%e 49, 61, 127, 193, 271, 343, 421, 483, 559, 631

%e 63, 67, 163, 247, 339, 427, 519, 607, 691, 793

%e 79, 87, 187, 303, 403, 523, 639, 739, 853, 963

%o (Scheme)

%o (define (A278505 n) (A278505bi (A002260 n) (A004736 n)))

%o (define (A278505bi row col) (if (= 1 col) (A000960 row) (A278507bi row (- col 1)))) ;; Code for A278507bi given in A278507.

%Y Inverse: A278506.

%Y Transpose: A278503.

%Y Column 1: A000960, column 2: A100287 (apart from its initial 1), A099259 (differences).

%Y Cf. A278538 (row index of n), A278539 (column index of n).

%Y Cf. also arrays A278507 and A278511 (different variants).

%Y Cf. also A255545 (an analogous array constructed for Lucky sieve).

%K nonn,tabl

%O 1,2

%A _Antti Karttunen_, Nov 23 2016