

A198388


Square root of first term of a triple of squares in arithmetic progression.


5



1, 2, 7, 3, 7, 4, 17, 14, 5, 1, 6, 14, 23, 7, 31, 21, 8, 34, 9, 28, 21, 10, 49, 17, 11, 47, 2, 12, 35, 23, 13, 28, 51, 46, 71, 14, 62, 42, 7, 15, 16, 41, 35, 17, 41, 49, 79, 3, 68, 18, 97, 19, 56, 7, 42, 20, 69, 98, 34, 21, 93, 31, 63, 22, 85, 94, 23, 49, 73
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OFFSET

1,2


COMMENTS

A198384(n) = a(n)^2.
A198439(n) = a(A198409(n)).
There is a connection to xy of Pythagorean triangles (x,y,z). See a comment on the primitive Pythagorean triangle case under A198441 which applies mutatis mutandis.  Wolfdieter Lang, May 23 2013


LINKS

Ray Chandler, Table of n, a(n) for n = 1..10000
Reinhard Zumkeller, Table of initial values
Keith Conrad, Arithmetic progressions of three squares


EXAMPLE

Connection to Pythagorean triangles: a(2) = 2 because (in the notation of the Zumkeller link) (u,v,w) = 2*(1,5,7) and the corresponding Pythagorean triangle is 2*((71)/2,(1+7)/2,5) = 2*(3,4,5) with xy = 2*(43) = 2.  Wolfdieter Lang, May 23 2013


PROG

(Haskell)
a198388 n = a198388_list !! (n1)
a198388_list = map (\(x, _, _) > x) ts where
ts = [(u, v, w)  w < [1..], v < [1..w1], u < [1..v1],
w^2  v^2 == v^2  u^2]


CROSSREFS

Sequence in context: A329333 A083119 A246163 * A334375 A011304 A196392
Adjacent sequences: A198385 A198386 A198387 * A198389 A198390 A198391


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Oct 24 2011


STATUS

approved



