Definition: "Brazilian" numbers ("les nombres brésiliens" in French)are numbers n such that exists a natural number k with 1<k< (n-1) such that
the representation of n in base k has all equal digits.
1.Prove that all even numbers above 6 are Brazilian numbers.
2. How many odd Brazilian numbers are there below 100?
Numbers that are in fact Brazilian have their appropriate base and the representation in that base listed.
The bug had been not allowing enough characters to cover bases so that 83 in base 42 looked like a 1, as null characters were appended during the base conversion process, so extra Brazilians were found, such as 83, that were not Brazilian in fact.
4
5
6
7 2 111
8 3 22
9
10 4 22
11
12 5 22
13 3 111
14 6 22
15 2 1111
16 7 22
17
18 5 33
19
20 9 22
21 4 111
22 10 22
23
24 5 44
25
26 3 222
27 8 33
28 6 44
29
30 9 33
31 2 11111
32 7 44
33 10 33
34 16 22
35 6 55
36 8 44
37
38 18 22
39 12 33
40 3 1111
41
42 4 222
43 6 111
44 10 44
45 8 55
46 22 22
47
48 7 66
49
50 9 55
51 16 33
52 12 44
53
54 8 66
55 10 55
56 13 44
57 7 111
58 28 22
59
60 9 66
61
62 5 222
63 2 111111
64 15 44
65 12 55
66 10 66
67
68 16 44
69 22 33
70 9 77
71
72 11 66
73 8 111
74 36 22
75 14 55
76 18 44
77 10 77
78 12 66
79
80 3 2222
81 26 33
82 40 22
83
84 11 77
85 4 1111
86 6 222
87 28 33
88 10 88
89
90 14 66
91 9 111
92 22 44
93 5 333
94 46 22
95 18 55
96 11 88
97
98 13 77
99 10 99
27 done
DefDbl A-Z
Dim crlf$, nlist$, nptr, closest, closelist$, lst$, stack(11), stacklvl
Dim frmla$(1 To 50), leadzeros
' pid=10902
Private Sub Form_Load()
Form1.Visible = True
Text1.Text = ""
crlf = Chr$(13) + Chr$(10)
For n = 4 To 99
found = 0
For k = 2 To n - 2
nb$ = base$(n, k)
match = 1
For i = 2 To Len(nb)
If Mid(nb, i, 1) <> Left(nb, 1) Then match = 0: Exit For
Next
If match Then found = 1: Exit For
Next
If found Then
Text1.Text = Text1.Text & n & Str(k) & " " & nb & crlf
If n Mod 2 = 1 Then ct = ct + 1
Else
Text1.Text = Text1.Text & n & crlf
End If
Next
Text1.Text = Text1.Text & crlf & ct & " done"
End Sub
Function base$(n, b)
v$ = ""
n2 = n
Do
d = n2 Mod b
n2 = n2 \ b
v$ = Mid("0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ", d + 1, 1) + v$
Loop Until n2 = 0
base$ = v$
End Function
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Posted by Charlie
on 2017-07-15 12:36:30 |
Program had a bug -- fixed it
