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Search: id:A118676
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| A118676 |
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Sequence allows us to find the solutions of the equation X^2+(X+79)^2=Y^2. |
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7
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| 0, 20, 161, 237, 341, 1140, 1580, 2184, 6837, 9401, 12921, 40040, 54984, 75500, 233561, 320661, 440237, 1361484, 1869140, 2566080, 7935501, 10894337, 14956401, 46251680, 63497040, 87172484, 269574737, 370088061, 508078661, 1571196900
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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+79,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)+158 with a(0)=0,a(1)=20,a(2)=161,a(3)=237, a(4)=341, a(5)=1140.
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MATHEMATICA
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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.
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CROSSREFS
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Sequence in context: A059601 A125357 A126515 this_sequence A067534 A041768 A056114
Adjacent sequences: A118673 A118674 A118675 this_sequence A118677 A118678 A118679
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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), May 19 2006
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