A087602 Primes occurring as larger side of Heronian triangle (sides are consecutive integers, area and inradius are integers).

3, 5, 53, 140453

Offset: 1

Author

Zak Seidov, Aug 07 2003

Keywords

• more
• nonn

Comments

Next term (if it exists) is greater than 10^10000. - Ray Chandler, Jul 04 2015

Examples

			a(3)=53 because 53, 52 and 51 are sides of Heronian triangle (area is 1170, inradius is 15).
		

References

• Mohammad K. Azarian, Circumradius and Inradius, Problem S125, Math Horizons, Vol. 15, Issue 4, April 2008, p. 32. Solution published in Vol. 16, Issue 2, November 2008, p. 32.

Crossrefs

Cf. A001353, A016064, A003500, A087601.

Formula

p, p-1 and p-2 are sides of Heronian triangle.

Primes p such that 3*(p-1)^2-12 is a square, i.e., p-1 belongs to A003500. - Max Alekseyev, May 14 2010