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Search: id:A130647
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| A130647 |
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Sequence allows us to find the solutions of the equation: X^2+(X+839)^2=Y^2. |
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1
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| 0, 60, 2241, 2517, 2821, 15180, 16780, 18544, 90517, 99841, 110121, 529600, 583944, 643860, 3088761, 3405501, 3754717, 18004644, 19850740, 21886120, 104940781, 115700617, 127563681, 611641720, 674354640
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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+839,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)+1678 with: a(0)=0,a(1)=60,a(2)=2241,a(3)=2517,a(4)=2821, a(5)=15180.
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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: A004364 A054623 A075908 this_sequence A062263 A075917 A058929
Adjacent sequences: A130644 A130645 A130646 this_sequence A130648 A130649 A130650
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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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