1 out of n oblivious transfer
The sender chooses log n pairs of secret keys (say, for encryption). Then, each number between 1 and n is naturally associated with a subset of exactly log n keys. The protocol then works by running log n 1-out-of-2 OTs where the receiver asks for the keys that are associated with its input (number between 1 and n). Finally, the sender encrypts each of the n messages with the subset of keys associated with the number (using encryption so that without all keys nothing is learned).
It is not difficult to formally prove the security of this using simulation (as long as the OT is secure for malicious adversaries, this is also secure for malicious adversaries).
This solution goes back to a paper by Benny Pinkas [1].
[1] Moni Naor and Benny Pinkas. 1999. Oblivious transfer and polynomial evaluation. In Proceedings of the thirty-first annual ACM symposium on Theory of Computing (STOC '99). Association for Computing Machinery, New York, NY, USA, 245–254. DOI:https://doi.org/10.1145/301250.301312