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

1,1

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

Links

Table of n, a(n) for n=1..11.

Example

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).

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:

Crossrefs

Cf. A000045, A080648.

Sequence in context: A072149 A001066 A099518 * A184855 A187336 A169582

Adjacent sequences: A280103 A280104 A280105 * A280107 A280108 A280109

Keyword

nonn,more

Author

Michel Lagneau, Dec 28 2016

Status

approved