A280106 Numbers k such that the half sum of the prime factors of Fibonacci(k) is a Fibonacci number.

3, 6, 8, 10, 14, 15, 22, 26, 30, 34, 94

Offset: 1

Author

Michel Lagneau, Dec 28 2016

Keywords

• nonn
• more

Comments

Or numbers k such that A080648(k)/2 is a Fibonacci number.

Is this sequence finite ?

a(12), if it exists is >5000. - Robert Price, Mar 02 2017

Examples

			10 is in the sequence because Fibonacci(10) = 5*11=> 5+11 = 2*8 = 2*F(6);
94 is in the sequence because Fibonacci(94) = 2971215073*6643838879 =>
2971215073+6643838879 = 2*4807526976 = 2*F(48).
		

Crossrefs

Cf. A000045, A080648.

Programs

Maple

with(numtheory):with(combinat,fibonacci):nn:=300:
for n from 3 to nn do:
  f:=fibonacci(n):x:=factorset(f):n0:=nops(x):
  s:=sum(‘x[i]’, ‘i’=1..n0):c:=s/2:
  x1:=sqrt(5*c^2-4):x2:=sqrt(5*c^2+4):
    if x1=floor(x1) or x2=floor(x2)
     then
     print(n):
     else
    fi:
od: