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A198389 Square root of second term of a triple of squares in arithmetic progression. 5
5, 10, 13, 15, 17, 20, 25, 26, 25, 29, 30, 34, 37, 35, 41, 39, 40, 50, 45, 52, 51, 50, 61, 53, 55, 65, 58, 60, 65, 65, 65, 68, 75, 74, 85, 70, 82, 78, 73, 75, 80, 85, 85, 85, 89, 91, 101, 87, 100, 90, 113, 95, 104, 97, 102, 100, 111, 122, 106, 105, 123, 109 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A198385(n) = a(n)^2.

A198440(n) = a(A198409(n)).

Apart from its initial 1, A001653 is a subsequence: for all n>1 exists an m such that A198388(m)=1 and a(m)=A001653(n). [observed by Zak Seidov, Reinhard Zumkeller, Oct 25 2011]

There is a connection to hypotenuses of Pythagorean triangles. See a comment for the primitive case on A198441 which applies here 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 triangle hypotenuses: a(20) = 10 because (in the notation of the Zumkeller link) (u,v,w) = 2*(1,5,7) and the Pythagorean triangle is 2*(x=(7-1)/2,y=(1+7)/2,5) = 2*(3,4,5) with hypotenuse 2*5 = 10. - Wolfdieter Lang, May 23 2013

PROG

(Haskell)

a198389 n = a198389_list !! (n-1)

a198389_list = map (\(_, x, _) -> x) ts where

   ts = [(u, v, w) | w <- [1..], v <- [1..w-1], u <- [1..v-1],

                   w^2 - v^2 == v^2 - u^2]

CROSSREFS

Sequence in context: A049197 A324928 A009000 * A057100 A304436 A009003

Adjacent sequences:  A198386 A198387 A198388 * A198390 A198391 A198392

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Oct 24 2011

STATUS

approved

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Last modified March 4 20:58 EST 2021. Contains 341811 sequences. (Running on oeis4.)