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A061409
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For each y >= 1 there are only finitely many values of x >= 1 such that x-y and x+y are both squares; list all such pairs (x,y) ordered by values of y; sequence gives x values.
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4
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5, 10, 17, 26, 13, 37, 50, 20, 65, 82, 29, 101, 122, 25, 40, 145, 170, 53, 197, 34, 226, 68, 257, 290, 45, 85, 325, 362, 41, 104, 401, 58, 442, 125, 485, 530, 52, 73, 148, 577, 626, 173, 677, 90, 730, 65, 200, 785, 842, 61, 109, 229, 901, 962
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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REFERENCES
| Donald D. Spencer, Computers in Number Theory, Computer Science Press, Rockville MD, 1982, pp. 130-131.
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FORMULA
| The solutions are given by x = r^2+2*r*k+2*k^2, y = 2*k*(k+r) with r >= 1, k >= 1. - N. J. A. Sloane (njas(AT)research.att.com), May 02 2001
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EXAMPLE
| Pairs are [5, 4], [10, 6], [17, 8], [26, 10], [13, 12], [37, 12], [50, 14], ... For example 5-4 = 1^2, 5+4 = 3^2.
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CROSSREFS
| Cf. A061408, A060829, A060830.
Sequence in context: A190550 A071978 A105705 * A193053 A098749 A034676
Adjacent sequences: A061406 A061407 A061408 * A061410 A061411 A061412
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KEYWORD
| nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), May 01 2001
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