04_digits.tex

Paper X: Universal Residual Seeds and Conditional Occupied-System Completion

04_digits.tex

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \node[font=\small,align=center,font=\scriptsize] at (4.2,4.45) {$5^{0}$};
4 \node[font=\small,align=center,font=\scriptsize] at (5.35,4.45) {$5^{1}$};
5 \node[font=\small,align=center,font=\scriptsize] at (6.5,4.45) {$5^{2}$};
6 \node[font=\small,align=center,font=\scriptsize] at (7.65,4.45) {$5^{3}$};
7 \node[font=\small,align=center,font=\scriptsize] at (8.8,4.45) {$5^{4}$};
8 \node[font=\small,align=center,font=\scriptsize] at (9.95,4.45) {$5^{5}$};
9 \node[font=\small,align=center,anchor=east] at (2.4,3.85) {$x_{1}=4$};
10 \path[draw=black!25,fill=black!12] (3.65,3.58) rectangle (4.75,4.06);
11 \node[font=\small,align=center,font=\scriptsize] at (4.2,3.83) {$4$};
12 \path[draw=black!25,fill=white] (4.8,3.58) rectangle (5.9,4.06);
13 \node[font=\small,align=center,font=\scriptsize] at (5.35,3.83) {\textemdash};
14 \path[draw=black!25,fill=white] (5.95,3.58) rectangle (7.05,4.06);
15 \node[font=\small,align=center,font=\scriptsize] at (6.5,3.83) {\textemdash};
16 \path[draw=black!25,fill=white] (7.1,3.58) rectangle (8.2,4.06);
17 \node[font=\small,align=center,font=\scriptsize] at (7.65,3.83) {\textemdash};
18 \path[draw=black!25,fill=white] (8.25,3.58) rectangle (9.35,4.06);
19 \node[font=\small,align=center,font=\scriptsize] at (8.8,3.83) {\textemdash};
20 \path[draw=black!25,fill=white] (9.4,3.58) rectangle (10.5,4.06);
21 \node[font=\small,align=center,font=\scriptsize] at (9.95,3.83) {\textemdash};
22 \node[font=\small,align=center,anchor=east] at (2.4,3.23) {$x_{2}=19$};
23 \path[draw=black!25,fill=black!12] (3.65,2.96) rectangle (4.75,3.44);
24 \node[font=\small,align=center,font=\scriptsize] at (4.2,3.21) {$4$};
25 \path[draw=black!25,fill=black!12] (4.8,2.96) rectangle (5.9,3.44);
26 \node[font=\small,align=center,font=\scriptsize] at (5.35,3.21) {$3$};
27 \path[draw=black!25,fill=white] (5.95,2.96) rectangle (7.05,3.44);
28 \node[font=\small,align=center,font=\scriptsize] at (6.5,3.21) {\textemdash};
29 \path[draw=black!25,fill=white] (7.1,2.96) rectangle (8.2,3.44);
30 \node[font=\small,align=center,font=\scriptsize] at (7.65,3.21) {\textemdash};
31 \path[draw=black!25,fill=white] (8.25,2.96) rectangle (9.35,3.44);
32 \node[font=\small,align=center,font=\scriptsize] at (8.8,3.21) {\textemdash};
33 \path[draw=black!25,fill=white] (9.4,2.96) rectangle (10.5,3.44);
34 \node[font=\small,align=center,font=\scriptsize] at (9.95,3.21) {\textemdash};
35 \node[font=\small,align=center,anchor=east] at (2.4,2.61) {$x_{3}=94$};
36 \path[draw=black!25,fill=black!12] (3.65,2.34) rectangle (4.75,2.82);
37 \node[font=\small,align=center,font=\scriptsize] at (4.2,2.59) {$4$};
38 \path[draw=black!25,fill=black!12] (4.8,2.34) rectangle (5.9,2.82);
39 \node[font=\small,align=center,font=\scriptsize] at (5.35,2.59) {$3$};
40 \path[draw=black!25,fill=black!12] (5.95,2.34) rectangle (7.05,2.82);
41 \node[font=\small,align=center,font=\scriptsize] at (6.5,2.59) {$3$};
42 \path[draw=black!25,fill=white] (7.1,2.34) rectangle (8.2,2.82);
43 \node[font=\small,align=center,font=\scriptsize] at (7.65,2.59) {\textemdash};
44 \path[draw=black!25,fill=white] (8.25,2.34) rectangle (9.35,2.82);
45 \node[font=\small,align=center,font=\scriptsize] at (8.8,2.59) {\textemdash};
46 \path[draw=black!25,fill=white] (9.4,2.34) rectangle (10.5,2.82);
47 \node[font=\small,align=center,font=\scriptsize] at (9.95,2.59) {\textemdash};
48 \node[font=\small,align=center,anchor=east] at (2.4,1.99) {$x_{4}=469$};
49 \path[draw=black!25,fill=black!12] (3.65,1.72) rectangle (4.75,2.2);
50 \node[font=\small,align=center,font=\scriptsize] at (4.2,1.97) {$4$};
51 \path[draw=black!25,fill=black!12] (4.8,1.72) rectangle (5.9,2.2);
52 \node[font=\small,align=center,font=\scriptsize] at (5.35,1.97) {$3$};
53 \path[draw=black!25,fill=black!12] (5.95,1.72) rectangle (7.05,2.2);
54 \node[font=\small,align=center,font=\scriptsize] at (6.5,1.97) {$3$};
55 \path[draw=black!25,fill=black!12] (7.1,1.72) rectangle (8.2,2.2);
56 \node[font=\small,align=center,font=\scriptsize] at (7.65,1.97) {$3$};
57 \path[draw=black!25,fill=white] (8.25,1.72) rectangle (9.35,2.2);
58 \node[font=\small,align=center,font=\scriptsize] at (8.8,1.97) {\textemdash};
59 \path[draw=black!25,fill=white] (9.4,1.72) rectangle (10.5,2.2);
60 \node[font=\small,align=center,font=\scriptsize] at (9.95,1.97) {\textemdash};
61 \node[font=\small,align=center,anchor=east] at (2.4,1.37) {$x_{5}=2344$};
62 \path[draw=black!25,fill=black!12] (3.65,1.1) rectangle (4.75,1.58);
63 \node[font=\small,align=center,font=\scriptsize] at (4.2,1.35) {$4$};
64 \path[draw=black!25,fill=black!12] (4.8,1.1) rectangle (5.9,1.58);
65 \node[font=\small,align=center,font=\scriptsize] at (5.35,1.35) {$3$};
66 \path[draw=black!25,fill=black!12] (5.95,1.1) rectangle (7.05,1.58);
67 \node[font=\small,align=center,font=\scriptsize] at (6.5,1.35) {$3$};
68 \path[draw=black!25,fill=black!12] (7.1,1.1) rectangle (8.2,1.58);
69 \node[font=\small,align=center,font=\scriptsize] at (7.65,1.35) {$3$};
70 \path[draw=black!25,fill=black!12] (8.25,1.1) rectangle (9.35,1.58);
71 \node[font=\small,align=center,font=\scriptsize] at (8.8,1.35) {$3$};
72 \path[draw=black!25,fill=white] (9.4,1.1) rectangle (10.5,1.58);
73 \node[font=\small,align=center,font=\scriptsize] at (9.95,1.35) {\textemdash};
74 \node[font=\small,align=center,anchor=east] at (2.4,0.75) {$x_{6}=11719$};
75 \path[draw=black!25,fill=black!12] (3.65,0.48) rectangle (4.75,0.96);
76 \node[font=\small,align=center,font=\scriptsize] at (4.2,0.73) {$4$};
77 \path[draw=black!25,fill=black!12] (4.8,0.48) rectangle (5.9,0.96);
78 \node[font=\small,align=center,font=\scriptsize] at (5.35,0.73) {$3$};
79 \path[draw=black!25,fill=black!12] (5.95,0.48) rectangle (7.05,0.96);
80 \node[font=\small,align=center,font=\scriptsize] at (6.5,0.73) {$3$};
81 \path[draw=black!25,fill=black!12] (7.1,0.48) rectangle (8.2,0.96);
82 \node[font=\small,align=center,font=\scriptsize] at (7.65,0.73) {$3$};
83 \path[draw=black!25,fill=black!12] (8.25,0.48) rectangle (9.35,0.96);
84 \node[font=\small,align=center,font=\scriptsize] at (8.8,0.73) {$3$};
85 \path[draw=black!25,fill=black!12] (9.4,0.48) rectangle (10.5,0.96);
86 \node[font=\small,align=center,font=\scriptsize] at (9.95,0.73) {$3$};
87 \node[font=\small,align=center] at (11.95,3) {$4x_m-1$\\$=3\cdot5^m$};
88 \node[font=\small,align=center,font=\scriptsize] at (11.95,1.25) {digits already\\fixed never change};
89 \end{tikzpicture}

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