By tweaking the usual Binet formula for the Fibonacci numbers in terms of the golden ration ϕ, you can write a real-valued function F(x) of the real numbers that obeys:

F(x+2) = F(x) + F(x+1)

for all x, real or complex.

H/T @octonion, @AndrewM_Webb, @hvairinhos, @stephentyrone pic.twitter.com/NQGjguRcx9

— Greg Egan (@gregeganSF) November 24, 2019