On Hofstadter’s Married Functions
Thomas Stoll · The Fibonacci Quarterly · 2008
In this note we show that Hofstadter’s married functions generated by the intertwined system of recurrences a(0) = 1, b(0) = 0, b(n) = n − a(b(n − 1)), a(n) = n − b(a(n − 1)) has the solutions a(n) = ⎿(n + 1)ϕ−1⏌ + ε1(n) and b(n) = ⎿(n + 1)ϕ−1⏌ − ε2(n), where ϕ is the golden ratio and ε1,ε2 are indicator functions of Fibonacci numbers diminished by 1.