A198464 Consider triples a<=b<c where (a^2+b^2-c^2)/(c-a-b) = 3, ordered by a and then b; sequence gives c values.

4, 8, 13, 19, 9, 13, 26, 17, 34, 43, 14, 18, 53, 32, 64, 38, 76, 19, 23, 30, 89, 103, 59, 118, 24, 28, 42, 67, 134, 151, 35, 43, 169, 29, 33, 63, 94, 188, 104, 208, 47, 58, 229, 31, 34, 38, 84, 251, 56, 137, 274, 149, 298, 39, 43, 108, 323, 52, 71, 88, 349

Offset

1,1

Comments

See A198453.

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..61.

Ron Knott, Pythagorean Triples and Online Calculators.

Example

2*5 + 3*6 = 4*7
3*6 + 7*10 = 8*11
4*7 + 12*15 = 13*16
5*8 + 18*21 = 19*22
6*9 + 6*9 = 9*12
6*9 + 11*14 = 13*16

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-A198463, A198465-A198469.

Sequence in context: A312165 A312166 A312167 * A312168 A312169 A312170

Adjacent sequences: A198461 A198462 A198463 * A198465 A198466 A198467

Keyword

nonn

Author

Charlie Marion, Nov 26 2011

Status

approved