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Search: id:A130014
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| A130014 |
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Sequence allows us to find the solutions of the equation: X^2+(X+881)^2=Y^2. |
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+0
2
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| 0, 43, 2440, 2643, 2860, 16443, 17620, 18879, 97980, 104839, 112176, 573199, 613176, 655939, 3342976, 3575979, 3825220, 19486419, 20844460, 22297143, 113577300, 121492543, 129959400, 661979143, 708112560
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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+881,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)+1762 with: a(0)=0,a(1)=43,a(2)=2440,a(3)=2643,a(4)=2860, a(5)=16443.
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MAPLE
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For the equation: X^2+(X+K)^2=Y^2 with K=2*m^2-1, m>=2 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)=2m+1, a(2)=6*m^2-10m+4, a(3)=3K, a(4)=6*m^2+10m+4, a(5)=40*m^2-58m+21. Ex: K=7, 17, 31, 71, 97, 127, 199, 241, 337, 449, 577, 647, 881, 967, ...
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CROSSREFS
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Cf. A118673, A118674, A129836.
Adjacent sequences: A130011 A130012 A130013 this_sequence A130015 A130016 A130017
Sequence in context: A009987 A076572 A015258 this_sequence A015323 A110704 A060485
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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 15 2007
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