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

3, 5, 53, 140453

Offset

1,1

Comments

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

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.

Links

Table of n, a(n) for n=1..4.

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

Example

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

Crossrefs

Cf. A001353, A016064, A003500, A087601.

Sequence in context: A260223 A260225 A020462 * A086340 A248923 A155121

Adjacent sequences: A087599 A087600 A087601 * A087603 A087604 A087605

Keyword

more,nonn

Author

Zak Seidov, Aug 07 2003

Status

approved