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Search: id:A130610
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| A130610 |
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Sequence allows us to find the solutions of the equation: X^2+(X+359)^2=Y^2. |
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+0
1
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| 0, 40, 901, 1077, 1281, 6160, 7180, 8364, 36777, 42721, 49621, 215220, 249864, 290080, 1255261, 1457181, 1691577, 7317064, 8493940, 9860100, 42647841, 49507177, 57469741, 248570700, 288549840, 334959064
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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+359,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)+718 with: a(0)=0,a(1)=40,a(2)=901,a(3)=1077,a(4)=1281, a(5)=6160.
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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: A130607 A130608 A130609 this_sequence A130611 A130612 A130613
Sequence in context: A013348 A013349 A140220 this_sequence A004339 A004349 A016092
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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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