First 11 values of A121387 coincide with apparently unrelated new seq
Ray Chandler
rayjchandler at sbcglobal.net
Fri Jun 22 21:59:39 CEST 2007
> The open issue being the multiplicity of such
> solutions. The table I gave in seqfans through n=41
> shows a number of double solutions, i.e. semiprime
> Pythagorean triple hypotenuses in two different ways.
>
>
> What is the first triple solution?
>
> Perhaps I should make a seq of the first k-tuple
> solution of semiprime Pythagorean triple hypotenuses.
> Or pehaps not. Thought and feelings?
>
See formula (24) in the MathWorld article on Pythagorean Triples -
http://mathworld.wolfram.com/PythagoreanTriple.html
The number of ways a semiprime can be the hypotenuse of a primitive right triangle is one if the semiprime is of the
form p^2 and two if the semiprime is of the form p*q with p,q distinct primes. There can be no higher number of ways
for a semiprime.
You missed one of the ways for 65 - (33,56,65)
Ray
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