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 SUMUS (Posted on 2012-04-21)
Let S(k) = 2 + 3 + 5 + 7 + 11 + 13 ... + p(k) , p(k) being the k-th prime.
For what values of k is S(k) a palindrome?

Go as high as you can.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 computer solution Comment 1 of 1

10        repeat
20          P=nxtprm(P)
30          inc K
40          S=S+P
50          Sstr=cutspc(str(S))
60          Good=1
70          for I=1 to int(len(Sstr)/2)
80             if mid(Sstr,I,1)<>mid(Sstr,len(Sstr)+1-I,1) then Good=0
90          next
100          if Good then print K;P;S
110        until P=0

finds before being stopped manually (each line shows k, p(k), S(k)):

1  2  2
2  3  5
8  19  77
7693  78347  285080582
8510  87641  352888253
12941  139241  854848458
146134  1959253  137372273731
637571  9564097  2939156519392

which is enough to find:

From Sloane's OEIS (A038582, A038583, A038584)

`       k               p(k)                    S(k)           1                 2                         2             2                 3                         5             8                19                        77          7693             78347                 285080582          8510             87641                 352888253         12941            139241                 854848458        146134           1959253              137372273731        637571           9564097             2939156519392      27198825         516916921          6833383883833386      53205635        1048924213         27155268786255172    6283318531      155353386241     477749724515427947774    7167375533      178196630873     625179415050514971526  `

It would have taken quite a while for my computer to have reached this high.

 Posted by Charlie on 2012-04-21 14:12:08

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