A198458 Consider triples a<=b<c where (a^2+b^2-c^2)/(c-a-b) = 2, ordered by a and then b; sequence gives a values.

3, 4, 5, 6, 7, 7, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 18, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 26, 26, 27, 27, 27, 28, 28, 28, 28, 28, 29, 30, 30, 30, 30, 30, 30, 31, 31, 31

Offset

1,1

Comments

See A198453 and A198457.

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..71.

Ron Knott, Pythagorean Triples and Online Calculators.

Example

3*5 + 6*8 = 7*9
4*6 + 4*6 = 6*8
5*7 + 16*17 = 17*18
6*8 + 10*12 12*14
7*9 + 8*10 = 11*13
7*9 + 30*32 = 31*33

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-A198457, A198459-A198469.

Sequence in context: A196119 A385884 A225852 * A134483 A121151 A088243

Adjacent sequences: A198455 A198456 A198457 * A198459 A198460 A198461

Keyword

nonn

Author

Charlie Marion, Nov 15 2011

Status

approved