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A198390 Square root of third term of a triple of squares in arithmetic progression. 7
7, 14, 17, 21, 23, 28, 31, 34, 35, 41, 42, 46, 47, 49, 49, 51, 56, 62, 63, 68, 69, 70, 71, 73, 77, 79, 82, 84, 85, 89, 91, 92, 93, 94, 97, 98, 98, 102, 103, 105, 112, 113, 115, 119, 119, 119, 119, 123, 124, 126, 127, 133, 136, 137, 138, 140, 141, 142, 146 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A198386(n) = a(n)^2.

A198441(n) = a(A198409(n)).

There is a connection to the leg sums of Pythagorean triangles.

See a comment on the primitive case under A198439, which applies mutatis mutandis. - Wolfdieter Lang, May 23 2013

Are these just the positive multiples of A001132? - Charles R Greathouse IV, May 28 2013

LINKS

Table of n, a(n) for n=1..59.

Reinhard Zumkeller, Table of initial values

Keith Conrad, Arithmetic progressions of three squares

EXAMPLE

Connection to leg sums of Pythagorean triangles: a(2) = 14 because (in the notation of the Zumkeller link) (u,v,w)= (2,10,14) = 2*(1,5,7), and this corresponds to the non-primitive Pythagorean triangle 2*(x=(7-1)/1,y=(1+7)/2,z=5) = 2*(3,4,5) with leg sum 2*(3+4) = 14. - Wolfdieter Lang, May 23 2013

PROG

(Haskell)

a198390 n = a198390_list !! (n-1)

a198390_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]

(PARI) is(n)=my(t=n^2); forstep(i=2-n%2, n-2, 2, if(issquare((t+i^2)/2), return(1))); 0 \\ Charles R Greathouse IV, May 28 2013

CROSSREFS

Sequence in context: A269173 A167197 A100599 * A118905 A254064 A257224

Adjacent sequences:  A198387 A198388 A198389 * A198391 A198392 A198393

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Oct 24 2011

STATUS

approved

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Last modified November 21 17:44 EST 2017. Contains 295004 sequences.