A280106 - OEIS

%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