On Golomb′s Self Describing Sequence Original Research Article

A proof of the oscillation estimate E(n)=Ω±(nφ−1−ε) is given, where E(n)colon, equalsF(n)−φ2−φnφ−1 and F is the nondecreasing "self describing" sequence 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9… defined by F(1)=1 and F(n)={m:F(m)=n}.