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In[]:=
NestGraph[n{2n,n+1},0,16]
Out[]=
In[]:=
ResourceFunction["GraphNeighborhoodVolumes"][NestGraph[n{2n,n+1},0,12]]
In[]:=
First[Values[%53]]
Out[]=
{1,2,3,5,8,13,21,34,55,89,144,233,377}
In[]:=
ResourceFunction["RaggedMeanAround"][Values[%53]]
Out[]=
{1,2.991
±
0.006
,6.57±
0.06
,11.97±
0.19
,19.8±
0.5
,29.6±
1.0
,42.2±
1.8
,57.8±
3.0
,76.±
5.
,95.±
7.
,113.±
9.
,122.±
9.
,129.±
9.
,133.±
8.
,146.±
9.
,154.±
9.
,160.±
9.
,171.±
9.
,175.±
9.
,179.±
9.
,189.±
9.
,199.±
10.
,203.±
9.
,206.±
9.
,215.±
9.
,218.±
9.
,221.±
8.
,230.±
8.
,239.±
8.
,242.±
8.
,244.±
7.
,252.±
7.
,254.±
7.
,256.±
6.
,265.±
7.
,273.±
7.
,281.±
7.
,284.±
7.
,286.±
7.
,293.±
7.
,295.±
6.
,297.±
6.
,305.±
6.
,313.±
6.
,315.±
6.
,318.±
5.
,325.±
4.
,329.5±
0.5
}In[]:=
ListLinePlot[%]
Out[]=
In[]:=
ResourceFunction["GraphNeighborhoodVolumes"][NestGraph[n{2n,n+1},0,14]];
In[]:=
ResourceFunction["RaggedMeanAround"][Values[%]]
Out[]=
{1,2.9967
±
0.0023
,6.60±
0.04
,12.05±
0.11
,19.96±
0.29
,30.1±
0.6
,43.0±
1.1
,59.4±
2.0
,79.6±
3.2
,101.±
5.
,125.±
7.
,151.±
9.
,177.±
12.
,191.±
12.
,204.±
13.
,214.±
12.
,236.±
14.
,246.±
14.
,256.±
14.
,273.±
14.
,283.±
14.
,292.±
14.
,309.±
15.
,326.±
16.
,335.±
16.
,344.±
16.
,360.±
16.
,369.±
16.
,378.±
16.
,395.±
16.
,412.±
17.
,421.±
17.
,429.±
16.
,443.±
17.
,448.±
16.
,454.±
16.
,467.±
16.
,481.±
17.
,494.±
17.
,499.±
17.
,504.±
17.
,516.±
17.
,521.±
17.
,525.±
16.
,537.±
17.
,550.±
17.
,554.±
16.
,558.±
16.
,570.±
16.
,574.±
16.
,578.±
15.
,590.±
15.
,602.±
16.
,614.±
16.
,618.±
15.
,622.±
15.
,633.±
15.
,636.±
14.
,640.±
14.
,651.±
14.
,662.±
14.
,666.±
13.
,669.±
13.
,680.±
13.
,683.±
12.
,686.±
12.
,697.±
12.
,708.±
13.
,719.±
13.
,730.±
14.
,734.±
13.
,737.±
13.
,747.±
13.
,750.±
13.
,753.±
13.
,763.±
13.
,773.±
13.
,776.±
13.
,779.±
12.
,789.±
12.
,791.±
12.
,794.±
11.
,804.±
12.
,815.±
12.
,825.±
12.
,828.±
12.
,831.±
11.
,841.±
11.
,843.±
11.
,846.±
11.
,856.±
10.
,867.±
9.
,870.±
9.
,874.±
9.
,885.±
7.
,891.5±
0.5
}In[]:=
ListLinePlot[%]
Out[]=
In[]:=
ResourceFunction["LogDifferences"][ResourceFunction["RaggedMeanAround"][Values[%61]]]
Out[]=
{1.5834
±
0.0011
,1.948±
0.014
,2.09±
0.04
,2.26±
0.08
,2.24±
0.14
,2.33±
0.22
,2.42±
0.32
,2.5±
0.4
,2.3±
0.6
,2.2±
0.8
,2.2±
1.0
,2.0±
1.1
,1.0±
1.2
,0.9±
1.3
,0.8±
1.3
,1.6±
1.3
,0.7±
1.4
,0.7±
1.4
,1.3±
1.5
,0.7±
1.5
,0.7±
1.5
,1.3±
1.5
,1.3±
1.6
,0.7±
1.6
,0.7±
1.7
,1.3±
1.7
,0.7±
1.7
,0.7±
1.7
,1.3±
1.7
,1.3±
1.8
,0.7±
1.8
,0.7±
1.8
,1.0±
1.8
,0.4±
1.8
,0.4±
1.8
,1.1±
1.8
,1.1±
1.9
,1.0±
1.9
,0.4±
1.9
,0.4±
1.9
,1.0±
1.9
,0.4±
2.0
,0.4±
1.9
,1.0±
1.9
,1.0±
2.0
,0.4±
2.0
,0.4±
1.9
,1.0±
1.9
,0.4±
1.9
,0.4±
1.9
,1.1±
1.9
,1.0±
1.9
,1.0±
1.9
,0.4±
1.9
,0.3±
1.9
,1.0±
1.9
,0.3±
1.9
,0.3±
1.8
,1.0±
1.8
,1.0±
1.8
,0.3±
1.8
,0.3±
1.7
,1.0±
1.7
,0.3±
1.7
,0.3±
1.6
,1.1±
1.7
,1.1±
1.7
,1.1±
1.8
,1.0±
1.8
,0.3±
1.8
,0.3±
1.8
,1.0±
1.8
,0.3±
1.8
,0.3±
1.8
,1.0±
1.8
,1.0±
1.8
,0.3±
1.8
,0.3±
1.8
,1.0±
1.7
,0.3±
1.7
,0.3±
1.7
,1.1±
1.7
,1.1±
1.7
,1.0±
1.7
,0.3±
1.7
,0.3±
1.7
,1.0±
1.7
,0.3±
1.6
,0.3±
1.6
,1.1±
1.6
,1.1±
1.5
,0.4±
1.4
,0.4±
1.4
,1.1±
1.2
,0.7±
0.7
}In[]:=
ListLinePlot[%]
Out[]=
In[]:=
ResourceFunction["GraphNeighborhoodVolumes"][NestGraph[n{2n,2n+1},0,12]];
In[]:=
ListLinePlot[ResourceFunction["LogDifferences"][ResourceFunction["RaggedMeanAround"][Values[%]]]]
Out[]=
QuotientRemainder Plots
QuotientRemainder Plots
Modulo
Modulo
Collatz without choice
Collatz without choice
Reversible 3n+1
Reversible 3n+1
Building integers from operations
Building integers from operations
Mod cases
Mod cases
Universal Arithmetic System
Universal Arithmetic System
Algebraic Number
Algebraic Number
UFDs?
UFDs?
< Like arithmetic series , or geometric series >
< Like arithmetic series , or geometric series >