An asymptotic intertwining of the undelayed and delayed Fibonacci   numbers
  The list of properties of Fibonacci numbers F(n) (with multifaceted relevance in physics) is complemented by an empirical observation that in combination with the "next" family of the "delayed Fibonacci" numbers G(n) called, for convenience, "Gibonacci numbers" here, both sets exhibit certain remarkable and fairly unexpected asymptotic mutual-bracketing properties. 
Miloslav Znojil