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%I #22 Mar 02 2017 23:06:34
%S 3,6,8,10,14,15,22,26,30,34,94
%N Numbers k such that the half sum of the prime factors of Fibonacci(k) is a Fibonacci number.
%C Or numbers k such that A080648(k)/2 is a Fibonacci number.
%C Is this sequence finite ?
%C a(12), if it exists is >5000. - _Robert Price_, Mar 02 2017
%e 10 is in the sequence because Fibonacci(10) = 5*11=> 5+11 = 2*8 = 2*F(6);
%e 94 is in the sequence because Fibonacci(94) = 2971215073*6643838879 =>
%e 2971215073+6643838879 = 2*4807526976 = 2*F(48).
%p with(numtheory):with(combinat,fibonacci):nn:=300:
%p for n from 3 to nn do:
%p f:=fibonacci(n):x:=factorset(f):n0:=nops(x):
%p s:=sum(‘x[i]’, ‘i’=1..n0):c:=s/2:
%p x1:=sqrt(5*c^2-4):x2:=sqrt(5*c^2+4):
%p if x1=floor(x1) or x2=floor(x2)
%p then
%p print(n):
%p else
%p fi:
%p od:
%Y Cf. A000045, A080648.
%K nonn,more
%O 1,1
%A _Michel Lagneau_, Dec 28 2016
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