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Search: id:A076294
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| A076294 |
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Consider all Pythagorean triples (X,X+7,Z); sequence gives Z values. |
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+0
4
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| 5, 7, 13, 17, 35, 73, 97, 203, 425, 565, 1183, 2477, 3293, 6895, 14437, 19193, 40187, 84145, 111865, 234227, 490433, 651997, 1365175, 2858453, 3800117, 7956823, 16660285, 22148705, 46375763
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OFFSET
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0,1
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COMMENT
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First two terms included for consistency with A076293.
For the generic case x^2+(x+p)^2=y^2 with p=2*m^2-1 a prime number in A066436, m>=2, the x values are given by the sequence defined by: a(n)=6*a(n-3)-a(n-6)+2p with a(1)=0, a(2)=2m+1, a(3)=6m^2-10m+4, a(4)=3p, a(5)=6m^2+10m+4, a(6)=40m^2-58m+21.Y values are given by the sequence defined by: b(n)=6*b(n-3)-b(n-6) with b(1)=p, b(2)=2*m^2+2m+1, b(3)=10m^2-14m+5, b(4)=5p, b(5)=10m^2+14m+5, b(6)=58m^2-82m+29. [From Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 09 2009]
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FORMULA
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a(n) =6a(n-3)-a(n-6) =sqrt((A076293(n)^2+49)/2) =sqrt(A076295(n)^2+A076296(n)^2). a(3n+1)=7*A001653(n).
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EXAMPLE
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17 is in the sequence as the hypotenuse of the (8,15,17) triangle.
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CROSSREFS
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Cf. A001653, A076293, A076295, A076296.
Sequence in context: A095283 A163385 A106069 this_sequence A073574 A092110 A086844
Adjacent sequences: A076291 A076292 A076293 this_sequence A076295 A076296 A076297
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Oct 05 2002
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