Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences

Abstract Automatic sequences are not suitable for cryptographic applications since both their subword complexity and expansion small, correlation measure of order 2 is large. These highly predictable despite having a large maximum complexity. However, recent results show that polynomial subsequences automatic sequences, such as the Thue–Morse sequence, better candidates pseudorandom sequences. A natural generalization morphic given by fixed point prolongeable morphism necessarily uniform. In this paper we prove lower bound sum digits function in Zeckendorf base which an example sequence. We also sequence keep complexity,