[seqfan] Simple sequence based on Pythagorean triples
jfb at brennen.net
Thu Dec 26 19:48:46 CET 2013
This sequence seems simple enough and yet is not in the OEIS:
Begin with a(0) = 3.
Let a(n) for n > 0 be the smallest positive integer not yet
in the sequence which forms part of a Pythagorean triple
when paired with a(n-1).
I believe that the sequence begins:
(Any typos are part of my cut-and-paste...)
Is the sequence infinite? Can it "paint itself into
a corner" at any point? Note that picking any starting
point >= 5 seems to lead to a finite sequence ending in
By beginning with 3 or 4, you make sure that the 5,3,4
dead-end is never available.
If infinite, is it a permutation of the integers >= 3?
It seems likely. Proving it doesn't seem easy though.
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