Find three different triplets of consecutive integers such that the first term of each triplet is a numerical palindrome, the second a square, and the third a prime.
DefDbl A-Z
Dim wd(10) As String, w As String, sz, crlf$
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
Private Sub Form_Load()
Text1.Text = ""
crlf$ = Chr(13) + Chr(10)
Form1.Visible = True
For n = 1 To 9999999
ns$ = LTrim(Str(n))
l = Len(ns$)
s1$ = ns$
For i = l To 1 Step -1
s1$ = s1$ + Mid(ns$, i, 1)
Next
GoSub checkIt
s1$ = ns$
For i = l - 1 To 1 Step -1
s1$ = s1$ + Mid(ns$, i, 1)
Next
GoSub checkIt
Next n
Text1.Text = Text1.Text & "done"
Exit Sub
checkIt:
sq = Val(s1$) + 1
sr = Int(Sqr(sq) + 0.5)
If sr * sr = sq Then
pr = sq + 1
If prmdiv(pr) = pr Then
Text1.Text = Text1.Text & s1$ & Str(sq) & Str(pr) & crlf
DoEvents
End If
End If
Return
End Sub
Function prm(i)
Dim p As Long
Open "17-bit primes.bin" For Random As #111 Len = 4
Get #111, i, p
prm = p
Close 111
End Function
Function prmdiv(num)
Dim n, dv, q
If num = 1 Then prmdiv = 1: Exit Function
n = Abs(num): If n > 0 Then limit = Sqr(n) Else limit = 0
If limit <> Int(limit) Then limit = Int(limit + 1)
dv = 2: GoSub DivideIt
dv = 3: GoSub DivideIt
dv = 5: GoSub DivideIt
dv = 7
Do Until dv > limit
GoSub DivideIt: dv = dv + 4 '11
GoSub DivideIt: dv = dv + 2 '13
GoSub DivideIt: dv = dv + 4 '17
GoSub DivideIt: dv = dv + 2 '19
GoSub DivideIt: dv = dv + 4 '23
GoSub DivideIt: dv = dv + 6 '29
GoSub DivideIt: dv = dv + 2 '31
GoSub DivideIt: dv = dv + 6 '37
Loop
If n > 1 Then prmdiv = n
Exit Function
DivideIt:
Do
q = Int(n / dv)
If q * dv = n And n > 0 Then
prmdiv = dv: Exit Function
Else
Exit Do
End If
Loop
Return
End Function
Function nxtprm(x)
Dim n
n = x + 1
While prmdiv(n) < n
n = n + 1
Wend
nxtprm = n
End Function
finds only
3 4 5
99 100 101
575 576 577
The seven digits of n would allow for 14-digit palindromes to lead off the triplet, so it looks as if the three triplets are all there are.
Edited on January 30, 2015, 10:35 am
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Posted by Charlie
on 2015-01-30 10:31:52 |
computer solution
