The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Cf. A159200, A159920. Sequence in context: A199435 A257898 A333286 * A310929 A310930 A131432 Adjacent sequences: A159916 A159917 A159918 * A159920 A159921 A159922 KEYWORD easy,nonn,tabl AUTHOR Russell Walsmith, Apr 25 2009 EXTENSIONS More terms from Philippe Deléham, May 11 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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