A159919 A square array of numbers, read by antidiagonals, called Sundaram's sieve.
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
Offset: 1
Examples
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)
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.
Programs
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Mathematica
A159919list[dmax_]:=Table[2k(j-k+1)+j+1,{j,dmax},{k,j}];A159919list[10] (* Generates 10 antidiagonals *) (* Paolo Xausa, Jul 26 2023 *)
Formula
For the term in row j and column k, we have T[j, k] = 2*j*k + j + k.
Extensions
More terms from Philippe Deléham, May 11 2009
Comments