A160238 Numbers n such that n^2 can be expressed as the sum of three different nonzero Fibonacci numbers.

3, 4, 5, 6, 7, 8, 9, 10, 12, 16, 17, 18, 20, 23, 24, 25, 32, 33, 35, 37, 40, 47, 57, 86, 112, 123, 139, 216, 322, 843, 1161, 1476, 2207, 3864, 4999, 5778, 15127, 39603, 103682, 271443, 710647, 1244196, 1860498, 4870847, 12752043

Offset

1,1

Comments

There exist a proper subsequence b(i)of a(n): n=[1, 2, 8, 17, 21, 24, 25, 28,29, 30, 31, 32, 33, 34, ...] such that approximatively b(i+1)=b(i)*(1+phi) where phi is 1.618... is the golden ratio and the approximation holds as a limit when i goes to infinity. For such a subsequence b(i) we have the following formula for the corresponding term when squared b(i)*b(i)=Fib(4*i+1)+Fib(4*i-1)+Fib(3). In the previous example 4999=b(9).

Links

Table of n, a(n) for n=1..45.

Example

4999*4999=24990001=Fib(37)+Fib(35)+Fib(3)

Crossrefs

Cf. A000045, A135709, A135558.

Sequence in context: A261793 A262288 A236681 * A039165 A138220 A137913

Adjacent sequences: A160235 A160236 A160237 * A160239 A160240 A160241

Keyword

nonn

Author

Carmine Suriano, May 05 2009

Extensions

Inserted 4 (with 4^2=13+1+2), 6 (with 36=21+2+13), 12 (with 12^2=89+21+34) etc. Added "nonzero" to definition - R. J. Mathar, Oct 23 2010

Status

approved