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Search: id:A130645
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| A130645 |
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Sequence allows us to find the solutions of the equation: X^2+(X+439)^2=Y^2. |
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| 0, 44, 1121, 1317, 1541, 7644, 8780, 10080, 45621, 52241, 59817, 266960, 305544, 349700, 1557017, 1781901, 2039261, 9076020, 10386740, 11886744, 52899981, 60539417, 69282081, 308324744, 352850640, 403806620
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OFFSET
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0,2
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COMMENT
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Consider all Pythagorean triples (X,X+439,Y) ordered by increasing Y; sequence gives X values.
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FORMULA
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a(n)=6*a(n-3)-a(n-6)+878 with: a(0)=0,a(1)=44,a(2)=1121,a(3)=1317,a(4)=1541, a(5)=7644.
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MAPLE
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For the equation: X^2+(X+K)^2=Y^2 with K=p^2-2, p>=5 and K is a prime number, the X values are given by the sequence defined by: a(n)=6*a(n-3)-a(n-6)+2K with: a(0)=0, a(1)=2p+2, a(2)=3*p^2-10p+8, a(3)=3K, a(4)=3*p^2+10p+8, a(5)=20*p^2-58p+42. Ex: K=23, 47, 79, 167, 223, 359, 439, 727, 839, ...
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CROSSREFS
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Cf. A118675, A118676.
Sequence in context: A010996 A004423 A114170 this_sequence A004340 A004295 A063821
Adjacent sequences: A130642 A130643 A130644 this_sequence A130646 A130647 A130648
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KEYWORD
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nonn
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AUTHOR
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Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Jun 20 2007
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