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<DIV><FONT face=Arial size=2>I propose you a modest participation to your
problem.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I have calculated all the the terms of iterated
partial sums of Fibonacci numbers and extracted the primes < 10^6 (the
maximum I can do) , with the following results:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>For n>29, no prime < 10^6</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>For n=3, 220 primes <10^6 (list joined, excel
format))</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>For 3<n<=29, besides the terms cited in your
message only 3 primes <10^6 : 6763 (k=6, n=12) 59281 (k=7 , n=19) 80979
(k=7 n=20)</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>In the limit of 10^6, most sequences for any given
k are void in primes</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Best regards</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Philippe LALLOUET</FONT></DIV></BODY></HTML>