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A278507 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), ...

%I A278507 #21 Jun 23 2020 14:33:25
%S A278507 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 A278507 85,73,43,16,41,69,97,111,121,99,61,18,47,81,115,145,159,151,127,67,
%U A278507 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 A278507 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 A278507 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 A278507 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%H A278507 <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%F A278507 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 A278507 The top left corner of the array:
%e A278507    2,   4,   6,   8,  10,  12,  14,  16,  18,   20
%e A278507    5,  11,  17,  23,  29,  35,  41,  47,  53,   59
%e A278507    9,  21,  33,  45,  57,  69,  81,  93, 105,  117
%e A278507   15,  37,  55,  75,  97, 115, 135, 157, 175,  195
%e A278507   25,  51,  85, 111, 145, 171, 205, 231, 265,  291
%e A278507   31,  73, 121, 159, 199, 243, 283, 327, 367,  409
%e A278507   43,  99, 151, 211, 267, 319, 379, 433, 487,  547
%e A278507   61, 127, 193, 271, 343, 421, 483, 559, 631,  699
%e A278507   67, 163, 247, 339, 427, 519, 607, 691, 793,  879
%e A278507   87, 187, 303, 403, 523, 639, 739, 853, 963, 1081
%o A278507 (Scheme)
%o A278507 (define (A278507 n) (A278507bi (A002260 n) (A004736 n)))
%o A278507 (define (A278507bi row col) (cond ((= 1 row) (* 2 col)) (else (A278492bi (- row 1) (+ -1 (* col (+ 1 row)))))))
%o A278507 ;; Code for A278492bi given in A278492.
%Y A278507 Transpose: A278508.
%Y A278507 This is array A278505 without its leftmost column, A000960.
%Y A278507 Column 1: A100287 (apart from its initial 1).
%Y A278507 Rows: A005843, A016969, A017629.
%Y A278507 Cf. A278529 (column index of n), A278538 (row index of n).
%Y A278507 Cf. A278492.
%Y A278507 Cf. A255543 for analogous array for Lucky sieve.
%K A278507 nonn,tabl
%O A278507 1,1
%A A278507 _Antti Karttunen_, Nov 23 2016