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A159919 A square array of numbers, read by antidiagonals, called Sundaram's sieve. 1
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

Table of n, a(n) for n=1..66.

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)

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

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Last modified April 5 02:28 EDT 2020. Contains 333238 sequences. (Running on oeis4.)