[seqfan] A227112

Lars Blomberg lars.blomberg at visit.se
Fri Oct 11 19:29:25 CEST 2013

A227112: Numbers n such that there exists two primes p and q where the area A of the triangle of sides (n, p, q) is an integer.

The result in A227112 shows a count of 57 entries for the 273 even n in the range 4-548.

A search over the same range where the smaller prime p is varied between 3 and pmax and q assumes all possible prime values that create a triangle yields the following:

pmax=997, count=104
pmax=9973, count=122
pmax=99991, count=129
pmax=999983, count=129

Could we expect to find solutions for all the 273 values of n by testing with still larger primes?
Or are there theoretical facts that says we cannot?
Should A227112 be augmented to include the 129 solutions find so far?

/Lars B

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