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Search: id:A130609
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| A130609 |
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Sequence allows us to find the solutions of the equation: X^2+(X+223)^2=Y^2. |
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1
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| 0, 32, 533, 669, 833, 3672, 4460, 5412, 21945, 26537, 32085, 128444, 155208, 187544, 749165, 905157, 1093625, 4366992, 5276180, 6374652, 25453233, 30752369, 37154733, 148352852, 179238480, 216554192, 864664325
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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+223,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)+446 with: a(0)=0,a(1)=32,a(2)=533,a(3)=669,a(4)=833, a(5)=3672.
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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: A130606 A130607 A130608 this_sequence A130610 A130611 A130612
Sequence in context: A084486 A010984 A022596 this_sequence A004417 A093751 A082557
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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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