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Square array where row n (n >= 0) gives the numbers remaining after the n-th round of the Flavius sieve, read by descending antidiagonals.
5

%I #22 Jan 02 2023 12:30:52

%S 1,2,1,3,3,1,4,5,3,1,5,7,7,3,1,6,9,9,7,3,1,7,11,13,13,7,3,1,8,13,15,

%T 15,13,7,3,1,9,15,19,19,19,13,7,3,1,10,17,21,25,25,19,13,7,3,1,11,19,

%U 25,27,27,27,19,13,7,3,1,12,21,27,31,31,31,27,19,13,7,3,1,13,23,31,37,39,39,39,27,19,13,7,3,1

%N Square array where row n (n >= 0) gives the numbers remaining after the n-th round of the Flavius sieve, read by descending antidiagonals.

%C The terms of square array A(row,col) are read by descending antidiagonals as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...

%H Antti Karttunen, <a href="/A278492/b278492.txt">Table of n, a(n) for n = 0..10439; the first 144 antidiagonals of the array</a>

%H D. Wilson et al., <a href="http://list.seqfan.eu/oldermail/seqfan/2016-November/thread.html">Interesting sequence</a>, SeqFan list, Nov. 2016

%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(n,k) = 1 + A278482(n,k).

%e The top left corner of the array:

%e 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (row 0: start from A000027)

%e 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 (after the 1st round, A005408 remain)

%e 1, 3, 7, 9, 13, 15, 19, 21, 25, 27 (after the 2nd, A047241)

%e 1, 3, 7, 13, 15, 19, 25, 27, 31, 37

%e 1, 3, 7, 13, 19, 25, 27, 31, 39, 43

%e 1, 3, 7, 13, 19, 27, 31, 39, 43, 49

%e 1, 3, 7, 13, 19, 27, 39, 43, 49, 61

%e 1, 3, 7, 13, 19, 27, 39, 49, 61, 63

%e 1, 3, 7, 13, 19, 27, 39, 49, 63, 67

%e 1, 3, 7, 13, 19, 27, 39, 49, 63, 79

%o (Scheme)

%o (define (A278492 n) (A278492bi (A002262 n) (A025581 n)))

%o (define (A278492bi row col) (+ 1 (A278482bi row col)))

%Y One more than A278482.

%Y Transpose: A278493.

%Y Rows: A000027, A005408, A047241, A056530, A056531.

%Y Main diagonal: A000960.

%Y Cf. A278507 (the numbers removed at each round).

%Y Similarly constructed arrays for other sieves: A258207, A260717.

%K nonn,tabl

%O 0,2

%A _Antti Karttunen_, Nov 23 2016, after _David W. Wilson_'s posting on SeqFan-list Nov 22 2016