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Search: id:A134588
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| A134588 |
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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. |
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+0
3
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OFFSET
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1,2
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COMMENT
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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.
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REFERENCES
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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.
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CROSSREFS
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Cf. A134587.
Sequence in context: A005225 A052929 A151415 this_sequence A000060 A089752 A007029
Adjacent sequences: A134585 A134586 A134587 this_sequence A134589 A134590 A134591
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KEYWORD
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nonn
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AUTHOR
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Shanzhen Gao (sgao2(AT)fau.edu), Nov 02 2007
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