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Search: id:A130017
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| A130017 |
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Sequence allows us to find the solutions of the equation: X^2+(X+967)^2=Y^2. |
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+0
2
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| 0, 45, 2688, 2901, 3128, 18105, 19340, 20657, 107876, 115073, 122748, 631085, 673032, 717765, 3680568, 3925053, 4185776, 21454257, 22879220, 24398825, 125046908, 133352201, 142209108, 728829125, 777235920
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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+967,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)+1934 with: a(0)=0,a(1)=45,a(2)=2688,a(3)=2901,a(4)=3128, a(5)=18105.
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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.
Sequence in context: A095658 A109941 A035097 this_sequence A025755 A113630 A004707
Adjacent sequences: A130014 A130015 A130016 this_sequence A130018 A130019 A130020
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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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