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NestGraph[n|->{2n,n+1},1,5,VertexLabels->Automatic]
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NestGraph[n|->{2n,n+1},1,10]
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NestGraph[n|->{2n,n+1},{1,2},2]
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NestGraph[n|->{2n,n+1},{2,3},3]
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NestGraph[n|->{2n,n+1},1,10,VertexLabelsAutomatic]
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Pentagon:
{n,n+1,2n,2n+1,2n+2}
Odd nodes: 3 edges
Even nodes: 4 edges
Even nodes: 4 edges
Seems to be a spiral
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UndirectedGraph[NestGraph[n|->{2n,n+1},1,10]]
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Other Cases
Other Cases
Since this is a linear function of n, it doesn’t matter whether we start from 1 or x.....
This compares the two branches of the cycle:
Iterating down two branches with
do these ever match?
This is the same as 2n , n + 1
In {a n, n+1} appears to be making (a+3)-gons.......
One branch gives powers of a; the other gives successive numbers....
In the ‘gons, claim is that there are two “a events”, and the others are all +1 events
Directions are all from smallest number as source, to largest number as sink [ inevitable because this rule only makes numbers larger ]
Other Cases
Other Cases
Shows which event is which:
The two “blue branches” correspond to:
These take a steps to match up “on the other side”
Agreement of iterations
Agreement of iterations
Basic question: when does a number first recur?
Length 3 + length 2 pentagon
Nested addition ; nested multiplication : both just powers
Non-interleaved case....