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Search: id:A130608
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| A130608 |
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Sequence allows us to find the solutions of the equation: X^2+(X+167)^2=Y^2. |
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1
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| 0, 28, 385, 501, 645, 2668, 3340, 4176, 15957, 19873, 24745, 93408, 116232, 144628, 544825, 677853, 843357, 3175876, 3951220, 4915848, 18510765, 23029801, 28652065, 107889048, 134227920, 166996876, 628823857
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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+167,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)+334 with: a(0)=0,a(1)=28,a(2)=385,a(3)=501,a(4)=645, a(5)=2668.
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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: A010944 A022623 A077507 this_sequence A126921 A035709 A035476
Adjacent sequences: A130605 A130606 A130607 this_sequence A130609 A130610 A130611
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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 17 2007
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