A198465 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, b and c values in that order.

3, 3, 4, 4, 6, 7, 5, 10, 11, 6, 7, 9, 6, 15, 16, 7, 10, 12, 7, 21, 22, 8, 28, 29, 9, 11, 14, 9, 36, 37, 10, 14, 17, 10, 22, 24, 10, 45, 46, 11, 27, 29, 11, 55, 56, 12, 15, 19, 12, 21, 24, 12, 66, 67, 13, 18, 22, 13, 25, 28, 13, 78, 79, 14, 45, 47, 14, 91, 92

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..69.

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: A342169 A187321 A145814 * A292836 A240116 A007768

Adjacent sequences: A198462 A198463 A198464 * A198466 A198467 A198468

Keyword

nonn

Author

Charlie Marion, Dec 19 2011

Status

approved