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%I A134588
%S A134588 1,2,3,10,27,98,120,327
%N A134588 A modified Heron sequence starting from 1, 2. 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 integers area.
%C A134588 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.
%D A134588 Heron Sequences, Paul Yiu, K. R. S. Sastry and Shanzhen Gao, presented 
               on the 2007 Integers Conference and submitted: INTEGERS - Electronic 
               Journal of Combinatorial Number Theory.
%Y A134588 Cf. A134587.
%Y A134588 Sequence in context: A005225 A052929 A151415 this_sequence A000060 A089752 
               A007029
%Y A134588 Adjacent sequences: A134585 A134586 A134587 this_sequence A134589 A134590 
               A134591
%K A134588 nonn
%O A134588 1,2
%A A134588 Shanzhen Gao (sgao2(AT)fau.edu), Nov 02 2007

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