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A159919 A square array of numbers, read by antidiagonals, called Sundaram's sieve.

%I A159919 #45 May 17 2025 10:48:05
%S A159919 4,7,7,10,12,10,13,17,17,13,16,22,24,22,16,19,27,31,31,27,19,22,32,38,
%T A159919 40,38,32,22,25,37,45,49,49,45,37,25,28,42,52,58,60,58,52,42,28,31,47,
%U A159919 59,67,71,71,67,59,47,31,34,52,66,76,82,84,82,76,66,52,34
%N A159919 A square array of numbers, read by antidiagonals, called Sundaram's sieve.
%C A159919 The sieve of Sundaram contains every number n > 3 for which the number 2*n + 1 is composite. For any n absent from this array, 2*n + 1 is a prime.
%C A159919 T[j, k] is the number of edges of the Cartesian product of the paths with j and k edges. - _Christian Barrientos_, May 14 2025
%D A159919 Ross Honsberger, Ingenuity in Mathematics, New Mathematical Library #23, Mathematical Association of America, 1970 (ISBN 0394709233); p. 75.
%D A159919 C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Oxford University Press, Inc., New York, 1966.
%H A159919 Paolo Xausa, <a href="/A159919/b159919.txt">Table of n, a(n) for n = 1..11325</a> (antidiagonals 1..150 of the array, flattened)
%H A159919 Andrew Baxter, <a href="http://banach.millersville.edu/~bob/math478/History/Sundaram.html">Sundaram's Sieve</a>.
%H A159919 Julian Havil, <a href="http://plus.maths.org/issue50/features/havil/index.html">Sundaram's Sieve</a>, Plus Magazine, March 2009.
%H A159919 New Zealand Maths, <a href="https://web.archive.org/web/20040309001101/www.nzmaths.co.nz/HelpCentre/Newsletter18.pdf">Newletter 18</a>, October 2002.
%H A159919 Wikipedia, <a href="http://en.wikipedia.org/wiki/Sieve_of_Sundaram">Sundaram's Sieve</a>.
%F A159919 For the term in row j and column k, we have T[j, k] = 2*j*k + j + k.
%e A159919 For the term in row 3 and column 3, we have T[3, 3] = 2*3*3 + 3 + 3 = 24. Thus, 2*T[3,3] + 1 = 49 is composite.
%e A159919 From _Petros Hadjicostas_, Jun 19 2019: (Start)
%e A159919 The square array begins as follows:
%e A159919    4,  7, 10, 13, 16, 19, ...
%e A159919    7, 12, 17, 22, 27, ...
%e A159919   10, 17, 24, 31, ...
%e A159919   13, 22, 31, ...
%e A159919   16, 27, ...
%e A159919   19, ...
%e A159919   ...
%e A159919 (End)
%t A159919 A159919list[dmax_]:=Table[2k(j-k+1)+j+1,{j,dmax},{k,j}];A159919list[10] (* Generates 10 antidiagonals *) (* _Paolo Xausa_, Jul 26 2023 *)
%Y A159919 Cf. A159200, A159920.
%K A159919 easy,nonn,tabl
%O A159919 1,1
%A A159919 _Russell Walsmith_, Apr 25 2009
%E A159919 More terms from _Philippe Deléham_, May 11 2009