4 problems

Let $\mathcal{S}$ be a binary sequence, and let $\lambda_{\mathcal{S}}(N)$ denote the binary logarithm of the least rational complexity of its first $N$ elements, equivalently the…

Let $p$ be an odd prime, and let $\mathcal L=(\ell_n)_{n\geq 0}$ be the $p$-periodic Legendre sequence associated with $f(X)=X$, with $\Phi_2(\mathcal L,N)$ its $N$th $2$-adic comp…

Let $\mathcal S=(s_n)_{n\geq 0}$ be one of the Thue–Morse sequences, the Rudin–Shapiro sequences along the values of $f(X)\in\{X,X^2,X^3,X^4\}$, or the binary sequence of the Zecke…

Legendre 2-adic-complexity conjecture.