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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
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
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
Sequence in context: A072149 A001066 A099518 * A184855 A187336 A169582
KEYWORD
nonn,more
AUTHOR
Michel Lagneau, Dec 28 2016
STATUS
approved