This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372266 #23 Jun 06 2024 12:46:27
%S A372266 2,3,4,7,11,21,44,107,292,861,2704,8946,30964,111611,417574,1617219,
%T A372266 6468832,26671628,113158082,493244584,2205856773,10108505566,
%U A372266 47413093736,227385209476,1113955476453,5569777382171,28400403557955,147572825753404,780881994429038
%N A372266 a(n) = floor((2*n - 3 + sqrt(1 + 8*(n - 2)!))/2).
%C A372266 An information-theoretic bound on the largest card deck with which one can perform an n-card trick in which the audience chooses two cards to hide.
%C A372266 The bound is based on the following argument: The assistant has (n-2)! ways to arrange the cards. This number can't be smaller than the number of potential guesses by the magician which is binomial(d - n + 2, 2), where d is the deck size.
%H A372266 Aria Chen, Tyler Cummins, Rishi De Francesco, Jate Greene, Tanya Khovanova, Alexander Meng, Tanish Parida, Anirudh Pulugurtha, Anand Swaroop, and Samuel Tsui, <a href="https://arxiv.org/abs/2405.21007">Card Tricks and Information</a>, arXiv:2405.21007 [math.HO], 2024. See p. 20.
%H A372266 Michael Kleber, <a href="https://web.northeastern.edu/seigen/11Magic/Articles/Best%20Card%20Trick.pdf">The best card trick</a>, The Mathematical Intelligencer 24 (2002), 9-11.
%e A372266 For n=3, the constraint on the deck size becomes: binomial(d-1, 2) can't exceed 1!=1. Thus a(3) = 3.
%t A372266 Table[Floor[(2 k - 3 + Sqrt[1 + 8 (k - 2)!])/2], {k, 2, 30}]
%Y A372266 Cf. A370888, A371217, A372255, A372256, A372264, A372265.
%K A372266 nonn
%O A372266 2,1
%A A372266 _Tanya Khovanova_ and the MIT PRIMES STEP junior group, Apr 24 2024