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A280106 Numbers k such that the half sum of the prime factors of Fibonacci(k) is a Fibonacci number. 0
3, 6, 8, 10, 14, 15, 22, 26, 30, 34, 94 (list; graph; refs; listen; history; text; internal format)
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(ā€˜x[i]ā€™, ā€˜iā€™=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

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Last modified July 30 13:24 EDT 2021. Contains 346359 sequences. (Running on oeis4.)