login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A198384(n) = a(n)^2.

A198439(n) = a(A198409(n)).

There is a connection to |x-y| 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*((7-1)/2,(1+7)/2,5) = 2*(3,4,5) with |x-y| = 2*(4-3) = 2. - Wolfdieter Lang, May 23 2013

PROG

(Haskell)

a198388 n = a198388_list !! (n-1)

a198388_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: A329333 A083119 A246163 * A334375 A011304 A196392

Adjacent sequences:  A198385 A198386 A198387 * A198389 A198390 A198391

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Oct 24 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 4 23:52 EST 2021. Contains 341812 sequences. (Running on oeis4.)