
COMMENTS

A modified Heron sequence is an increasing sequence such that every three consecutive terms (say u, v, w) of which determine a Heron triangle by using u+v, u+w and v+w as three sizes. A Heron triangle is a triangle with integer sides and integer area.
Given u<v be positive integers such that (u, v) is not (1, 4), (1, 9), (2, 8), (2, 18) or (4, 6). Then there is an integer w such that the three sizes u+v, u+w and v+w form a Heron triangle. Therefore infinite modified Heron sequence exists. We can construct arbitrarily long Heron sequences. However, it is still open whether an infinite Heron sequence exists.


LINKS

Table of n, a(n) for n=1..8.
Paul Yiu, K. R. S. Sastry and Shanzhen Gao, Heron Sequences, presented on the 2007 Integers Conference and INTEGERS  Electronic Journal of Combinatorial Number Theory, Article 16 Volume 9 Supplement (2009).
