The number of divisions of $\mathbb{R}^3$ by $k \ge 0$ planes in general position starts 1,2,4,8, then 15, etc. For $\mathbb{R}^6$ it is 1,2,4,8,16,32,64 then 127. In general for $\mathbb{R}^N$ it is the sum of the binomial coefficients from $\binom{k}{0}$ up to $\binom{k}{N}$ and hence it agrees with $2^k$ for terms 0,1,2, up to N before starting to fall off.
other answers Of course for prime p, $2^{p-1}=1 \mod p$ but there are only 2 known cases $p=1093$ and $3511$ where $2^{p-1}=1 \mod p^2$. SO primes and primes with $2^{p-1} \ne 1 mod p^2$ agree for the first 182 primes. For "listed in the OEIS there are a couple which go from 1 to 99 then skip 100.