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A198466 Consider triples a<=b<c where (a^2+b^2-c^2)/(c-a-b) = -1, ordered by a and then b; sequence gives a values. 0
3, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 28 (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..75.

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: A230113 A217031 A104136 * A212642 A159624 A036288

Adjacent sequences:  A198463 A198464 A198465 * A198467 A198468 A198469

KEYWORD

nonn

AUTHOR

Charlie Marion, Dec 19 2011

STATUS

approved

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Last modified August 17 23:58 EDT 2017. Contains 290682 sequences.