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A198440
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Square root of second term of a triple of squares in arithmetic progression that is not a multiple of another triple in (A198384, A198385, A198386).
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5
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5, 13, 17, 25, 29, 37, 41, 61, 53, 65, 65, 85, 73, 85, 89, 101, 113, 97, 109, 125, 145, 145, 149, 137, 181, 157, 173, 197, 185, 169, 221, 185, 193, 205, 229, 257, 265, 205, 221, 233, 241, 269, 313, 265, 293, 325, 277, 317, 281, 365, 289, 305, 305, 365, 401
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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A198436(n) = a(n)^2; a(n) = A198389(A198409(n)).
This sequence gives the hypotenuses of primitive Pythagorean triangles (with multiplicities) ordered according to nondecreasing values of the leg sums x+y (called w in the Zumkeller link, given by A198441). See the comment on the equivalence to primitive Pythagorean triangles in A198441. For the values of these hypotenuses ordered nondecreasingly see A020882. See also the triangle version A222946. - Wolfdieter Lang, May 23 2013
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LINKS
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Ray Chandler, Table of n, a(n) for n = 1..10000
Reinhard Zumkeller, Table of initial values
Keith Conrad, Arithmetic progressions of three squares
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EXAMPLE
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From Wolfdieter Lang, May 22 2013: (Start)
Primitive Pythagorean triangle (x,y,z), even y, connection:
a(8) = 61 because the leg sum x+y = A198441(8) = 71 and due to A198439(8) = 49 one has y = (71+49)/2 = 60 is even, hence x = (71-49)/2 = 11 and z = sqrt(11^2 + 60^2) = 61. (End)
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PROG
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(Haskell)
a198440 n = a198440_list !! (n-1)
a198440_list = map a198389 a198409_list
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CROSSREFS
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Cf. A020882, A222946.
Sequence in context: A008846 A162597 A120960 * A094194 A088511 A089545
Adjacent sequences: A198437 A198438 A198439 * A198441 A198442 A198443
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Oct 25 2011
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STATUS
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approved
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