%I #21 Jun 23 2020 14:33:25

%S 2,4,5,6,11,9,8,17,21,15,10,23,33,37,25,12,29,45,55,51,31,14,35,57,75,

%T 85,73,43,16,41,69,97,111,121,99,61,18,47,81,115,145,159,151,127,67,

%U 20,53,93,135,171,199,211,193,163,87,22,59,105,157,205,243,267,271,247,187,103,24,65,117,175,231,283,319,343,339,303,229,123

%N Square array A(row,col) where row n lists the numbers removed in round n of Flavius sieve. Array 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="/A278507/b278507.txt">Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of the array</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(1,col) = 2*col; for row > 1, A(row,col) = A278492(row-1,(col*(row+1))-1). [Note that unlike this array, A278492 uses zero-based indexing for its rows and columns.]

%e The top left corner of the array:

%e 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

%e 5, 11, 17, 23, 29, 35, 41, 47, 53, 59

%e 9, 21, 33, 45, 57, 69, 81, 93, 105, 117

%e 15, 37, 55, 75, 97, 115, 135, 157, 175, 195

%e 25, 51, 85, 111, 145, 171, 205, 231, 265, 291

%e 31, 73, 121, 159, 199, 243, 283, 327, 367, 409

%e 43, 99, 151, 211, 267, 319, 379, 433, 487, 547

%e 61, 127, 193, 271, 343, 421, 483, 559, 631, 699

%e 67, 163, 247, 339, 427, 519, 607, 691, 793, 879

%e 87, 187, 303, 403, 523, 639, 739, 853, 963, 1081

%o (Scheme)

%o (define (A278507 n) (A278507bi (A002260 n) (A004736 n)))

%o (define (A278507bi row col) (cond ((= 1 row) (* 2 col)) (else (A278492bi (- row 1) (+ -1 (* col (+ 1 row)))))))

%o ;; Code for A278492bi given in A278492.

%Y Transpose: A278508.

%Y This is array A278505 without its leftmost column, A000960.

%Y Column 1: A100287 (apart from its initial 1).

%Y Rows: A005843, A016969, A017629.

%Y Cf. A278529 (column index of n), A278538 (row index of n).

%Y Cf. A278492.

%Y Cf. A255543 for analogous array for Lucky sieve.

%K nonn,tabl

%O 1,1

%A _Antti Karttunen_, Nov 23 2016