A198461 Consider triples a<=b<c where (a^2+b^2-c^2)/(c-a-b) = 3, ordered by a and then b; sequence gives a, b and c values in that order.

2, 3, 4, 3, 7, 8, 4, 12, 13, 5, 18, 19, 6, 6, 9, 6, 11, 13, 6, 25, 26, 7, 15, 17, 7, 33, 34, 8, 42, 43, 9, 10, 14, 9, 15, 18, 9, 52, 53, 10, 30, 32, 10, 63, 64, 11, 36, 38, 11, 75, 76, 12, 14, 19, 12, 19, 23, 12, 27, 30, 12, 88, 89, 13, 102, 103, 14, 57, 59, 14, 117, 118

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..72.

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-A198460, A198462-A198469.

Sequence in context: A048259 A374911 A324150 * A379739 A228576 A390031

Adjacent sequences: A198458 A198459 A198460 * A198462 A198463 A198464

Keyword

nonn,tabf

Author

Charlie Marion, Nov 26 2011

Status

approved