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!)
A198468 Consider triples a<=b<c where (a^2+b^2-c^2)/(c-a-b) = -1, ordered by a and then b; sequence gives c values. 1
4, 7, 11, 9, 16, 12, 22, 29, 14, 37, 17, 24, 46, 29, 56, 19, 24, 67, 22, 28, 79, 47, 92, 21, 24, 37, 54, 106, 27, 42, 121, 137, 29, 53, 78, 154, 32, 59, 87, 172, 41, 50, 191, 34, 45, 55, 72, 211, 37, 42, 79, 117, 232, 128, 254, 39, 94, 277, 42, 63, 102, 301 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The definition can be generalized to define Pythagorean k-triples a<=b<c where (a^2+b^2-c^2)/(c-a-b)=k, or where for some integer k, a(a+k) + b(b+k) = c(c+k).  See A198453 for more about Pythagorean k-triples.

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.

LINKS

Table of n, a(n) for n=1..62.

Ron Knott, Pythagorean Triples and Online Calculators

EXAMPLE

3*2 + 3*2 = 4*3

4*3 + 6*5 = 7*6

5*4 + 10*9 = 11*10

6*5 + 7*6 = 9*8

6*5 + 15*14 = 16*15

PROG

(True BASIC)

input k

for a = (abs(k)-k+4)/2 to  40

for b = a to (a^2+abs(k)*a+2)/2

  let t = a*(a+k)+b*(b+k)

   let c =int((-k+ (k^2+4*t)^.5)/2)

    if c*(c+k)=t then print a; b; c,

next b

print

next a

end

CROSSREFS

Cf. A103606, A198453-A198469.

Sequence in context: A071084 A175833 A171964 * A032547 A075630 A274341

Adjacent sequences:  A198465 A198466 A198467 * A198469 A198470 A198471

KEYWORD

nonn

AUTHOR

Charlie Marion, Dec 19 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 January 24 01:05 EST 2020. Contains 331178 sequences. (Running on oeis4.)