

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
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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



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.
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(jk+1)+j+1, {j, dmax}, {k, j}]; A159919list[10] (* Generates 10 antidiagonals *) (* Paolo Xausa, Jul 26 2023 *)


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STATUS

approved



