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 What's Seven Got To Do With It? (Posted on 2018-05-14)
A simple algorithm generates the following sequence.

7, 115, 1411, 17141, 227721, 2757061, 35526761, ____?____

What number comes next?

 See The Solution Submitted by Larry Rating: 3.0000 (1 votes)

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 computer extension Comment 2 of 2 |
None of the digits is over 7, indicating the numbers might very well be base-8. In base-10 the numbers seem to be rep-7's, so the table below lists the base-8 representation of the first fifteen numbers that consist solely of 7's in base 10.

From the table we see the next value, represented by the question mark is 450545561.

Larry's previously posted problem's involvement with other another base (for pi) was a helpful hint in directing thinking toward, this time, base 8.

7    7
77    115
777    1411
7777    17141
77777    227721
777777    2757061
7777777    35526761
77777777    450545561
777777777    5626771161
7777777777    71745674161
77777777777    1103372532161
777777777777    13242712606161
7777777777777    161134753476161
77777777777777    2153641464156161
777777777777777    26066120012116161

DefDbl A-Z
Dim crlf\$

Form1.Visible = True
Text1.Text = ""
crlf = Chr(13) + Chr(10)

For i = 1 To 15
n = n * 10 + 7
Text1.Text = Text1.Text & n & "    " & base\$(n, 8) & crlf
Next i

Text1.Text = Text1.Text & crlf & " done"

End Sub

Function base\$(n, b)
v\$ = ""
n2 = n
Do
q = Int(n2 / b)
d = n2 - q * b
n2 = q
v\$ = Mid("0123456789abcdefghijklmnopqrstuvwxyz", d + 1, 1) + v\$
Loop Until n2 = 0
base\$ = v\$
End Function

Function fromBase(n\$, b)
v = 0
For i = 1 To Len(n\$)
c\$ = LCase\$(Mid(n\$, i, 1))
If c\$ > " " Then
v = v * b + InStr("0123456789abcdefghijklmnopqrstuvwxyz", c\$) - 1
End If
Next
fromBase = v
End Function

 Posted by Charlie on 2018-05-14 10:33:42

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