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Search: id:A061408
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| A061408 |
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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 y values. |
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5
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| 4, 6, 8, 10, 12, 12, 14, 16, 16, 18, 20, 20, 22, 24, 24, 24, 26, 28, 28, 30, 30, 32, 32, 34, 36, 36, 36, 38, 40, 40, 40, 42, 42, 44, 44, 46, 48, 48, 48, 48, 50, 52, 52, 54, 54, 56, 56, 56, 58, 60, 60, 60, 60, 62, 64, 64, 64, 66, 66, 68, 68, 70, 70, 72
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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Donald D. Spencer, Computers in Number Theory, Computer Science Press, Rockville MD, 1982, pp. 130-131.
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FORMULA
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The solutions are given by x = r^2+2*r*k+2*k^2, y = 2*k*(k+r) with r >= 1, k >= 1. - njas, May 02 2001
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EXAMPLE
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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
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Cf. A061409, A060829, A060830.
Sequence in context: A090967 A075254 A139203 this_sequence A063287 A134331 A090334
Adjacent sequences: A061405 A061406 A061407 this_sequence A061409 A061410 A061411
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KEYWORD
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nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), May 01 2001
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