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Search: id:A130646
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| A130646 |
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Sequence allows us to find the solutions of the equation: X^2+(X+727)^2=Y^2. |
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1
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| 0, 56, 1925, 2181, 2465, 13056, 14540, 16188, 77865, 86513, 96117, 455588, 505992, 561968, 2657117, 2950893, 3277145, 15488568, 17200820, 19102356, 90275745, 100255481, 111338445, 526167356, 584333520, 648929768
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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+727,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)+1454 with: a(0)=0,a(1)=56,a(2)=1925,a(3)=2181,a(4)=2465, a(5)=13056.
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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.
Adjacent sequences: A130643 A130644 A130645 this_sequence A130647 A130648 A130649
Sequence in context: A140406 A075512 A000504 this_sequence A038649 A004375 A103726
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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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