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 Pentagonal triple triangles (Posted on 2016-07-01)
Which triangular numbers are three times a pentagonal number?

Is there a geometrical interpretation to this?

 No Solution Yet Submitted by Jer No Rating

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 re: computer method (the part that wouldn't fit) | Comment 3 of 4 |
(In reply to computer method by Charlie)

The kth triangular number is 3 times a pentagonal number if k = 2 mod 3.

DefDbl A-Z
Dim crlf\$

Form1.Visible = True

Text1.Text = ""
crlf = Chr\$(13) + Chr\$(10)

For n = 1 To 1000
DoEvents
p = (3 * n * n - n) / 2
tr = 3 * p
Text1.Text = Text1.Text & mform(n, "####0") & mform(p, "#########0") & mform(p * 3, "#########0") & mform(isTri(tr), "######0") & crlf
Next

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

End Sub

Function isTri(t)
n = Int(Sqr(t * 2))
np = n + 1
If n * np = 2 * t Then isTri = n Else isTri = 0
End Function

Function mform\$(x, t\$)
a\$ = Format\$(x, t\$)
If Len(a\$) < Len(t\$) Then a\$ = Space\$(Len(t\$) - Len(a\$)) & a\$
mform\$ = a\$
End Function

 Posted by Charlie on 2016-07-01 10:14:21

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