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A159919 A square array of numbers, read by antidiagonals, called Sundaram's sieve. 4
4, 7, 7, 10, 12, 10, 13, 17, 17, 13, 16, 22, 24, 22, 16, 19, 27, 31, 31, 27, 19, 22, 32, 38, 40, 38, 32, 22, 25, 37, 45, 49, 49, 45, 37, 25, 28, 42, 52, 58, 60, 58, 52, 42, 28, 31, 47, 59, 67, 71, 71, 67, 59, 47, 31, 34, 52, 66, 76, 82, 84, 82, 76, 66, 52, 34 (list; table; graph; refs; listen; history; text; internal format)
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
Sequence in context: A199435 A257898 A333286 * A310929 A310930 A131432
KEYWORD
easy,nonn,tabl
AUTHOR
Russell Walsmith, Apr 25 2009
EXTENSIONS
More terms from Philippe Deléham, May 11 2009
STATUS
approved

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Last modified May 19 14:45 EDT 2024. Contains 372698 sequences. (Running on oeis4.)