OFFSET
1,1
COMMENTS
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.
REFERENCES
Ross Honsberger, Ingenuity in Mathematics, New Mathematical Library #23, Mathematical Association of America, 1970 (ISBN 0394709233); p. 75.
C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Oxford University Press, Inc., New York, 1966.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..11325 (antidiagonals 1..150 of the array, flattened)
Andrew Baxter, Sundaram's Sieve.
Julian Havil, Sundaram's Sieve, Plus Magazine, March 2009.
New Zealand Maths, Newletter 18, October 2002.
Wikipedia, Sundaram's Sieve.
FORMULA
For the term in row j and column k, we have T[j, k] = 2*j*k + j + k.
EXAMPLE
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.
From Petros Hadjicostas, Jun 19 2019: (Start)
The square array begins as follows:
4, 7, 10, 13, 16, 19, ...
7, 12, 17, 22, 27, ...
10, 17, 24, 31, ...
13, 22, 31, ...
16, 27, ...
19, ...
...
(End)
MATHEMATICA
A159919list[dmax_]:=Table[2k(j-k+1)+j+1, {j, dmax}, {k, j}]; A159919list[10] (* Generates 10 antidiagonals *) (* Paolo Xausa, Jul 26 2023 *)
CROSSREFS
KEYWORD
AUTHOR
Russell Walsmith, Apr 25 2009
EXTENSIONS
More terms from Philippe Deléham, May 11 2009
STATUS
approved