OFFSET
1,2
COMMENTS
1, 3, 5 and 21 are Fibonacci numbers. Are there other Fibonacci numbers in this sequence?
For a similar question and related proof attempt see the paper in the links section of A272412.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..734
EXAMPLE
3 is a term because 3 is divisible by 1 and 3. Average of 3 and 1 is 2 that is a Fibonacci number.
MATHEMATICA
s = Array[Fibonacci, {28}]; Select[Range@ Max@ s, MemberQ[s, Mean@ Divisors@ #] &] (* Michael De Vlieger, Apr 29 2016 *)
PROG
(PARI) isFibonacci(n)=my(k=n^2); k+=((k + 1) << 2); issquare(k) || (n > 0 && issquare(k-8))
is(n)=my(f=factor(n), s=sigma(f), d=numdiv(f)); s%d==0 && isFibonacci(s/d) \\ Charles R Greathouse IV, May 02 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Altug Alkan, Apr 29 2016
STATUS
approved