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Special palindromes (Posted on 2012-05-11) Difficulty: 4 of 5
The 5th prime multiplied by 5 is a palindrome (5*11=55).
Find additional numbers n such that when multiplied by the nth prime create a palindrome.
Exclude the trivial cases of n=1 and n=2.

See The Solution Submitted by Ady TZIDON    
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Solution computer solution (spoilers) | Comment 1 of 2
   10   repeat
   20    inc N:P=nxtprm(P)
   30    Prod=N*P
   40    Prs=cutspc(str(Prod))
   50    Good=1
   60    for I=1 to int(len(Prs)/2)
   70       if mid(Prs,I,1)<>mid(Prs,len(Prs)+1-I,1) then Good=0
   80    next
   90    if Good then print N,P,Prod
  100   until P=0
finds
    n          nth prime            product
      1                2                     2
      2                3                     6
      5               11                    55
     12               37                   444
     16               53                   848
   3623            33827             122555221
   4119            39119             161131161
 618725          9260479         5729689869275
 708567         10708871         7587952597857
1498739         23858227        35757255275753
before being stopped manually.
 

Using these numbers to look up the sequences in Sloane's OEIS gives one more example:

 A084122       A084121           A084123
2762990591   65941772591 182196497222794691281

  Posted by Charlie on 2012-05-11 14:06:26
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