In[]:=
Clear[n]​​n=10;​​mysparse=SparseArray[{{i_,i_}PrimePi[i+i],{i_,j_}/;(i==j+1)->PrimePi[i+j+1],{i_,j_}/;(i+1==j)->PrimePi[i+j+1]},{n,n}]//Normal;​​Through[{MatrixForm,MatrixPlot}@mysparse]
Out[]=

1
2
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
3
3
4
0
0
0
0
0
0
0
0
4
4
4
0
0
0
0
0
0
0
0
4
4
5
0
0
0
0
0
0
0
0
5
5
6
0
0
0
0
0
0
0
0
6
6
6
0
0
0
0
0
0
0
0
6
6
7
0
0
0
0
0
0
0
0
7
7
8
0
0
0
0
0
0
0
0
8
8
,

In[]:=
GraphPlot[AdjacencyGraph[mysparse],Method->"CircularEmbedding"]
Out[]=
In[]:=
n=30;​​mysparse=SparseArray[{{i_,i_}PrimePi[i+i],{i_,j_}/;(i==j+1)->PrimePi[i+j+1],{i_,j_}/;(i+1==j)->PrimePi[i+j+1]},{n,n}]//Normal;​​Through[{MatrixForm,MatrixPlot}@mysparse]
Out[]=

1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
4
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
4
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
5
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
6
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
6
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
7
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
8
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
8
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
9
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
9
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
9
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
10
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
11
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
11
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
11
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
12
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
12
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13
13
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
14
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
14
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
15
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
15
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
15
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
16
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
16
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
16
17
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
17
17
,

In[]:=
GraphPlot[AdjacencyGraph[mysparse],Method->"CircularEmbedding"]
Out[]=
Manipulate[​​Column[Through[{MatrixForm,MatrixPlot}@(SparseArray[{{i_,i_}PrimePi[i+i],{i_,j_}/;(i==j+1)->PrimePi[i+j+1],{i_,j_}/;(i+1==j)->PrimePi[i+j+1]},{n,n}]//Normal)]],​​{{n,10},1,50,1}]
Out[]=
​
n
1
2
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
3
3
4
0
0
0
0
0
0
0
0
4
4
4
0
0
0
0
0
0
0
0
4
4
5
0
0
0
0
0
0
0
0
5
5
6
0
0
0
0
0
0
0
0
6
6
6
0
0
0
0
0
0
0
0
6
6
7
0
0
0
0
0
0
0
0
7
7
8
0
0
0
0
0
0
0
0
8
8