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 A232894 #26 Jan 04 2018 03:51:52
%S A232894 1,5,4,11,16,13,31,27,18,22,34,52,45,45,31,112,57,73,113,99,64,77,114,
%T A232894 215,134,106,89,99,127,209,161,239,135,178,96,207,185,172,157,231,174,
%U A232894 195,309,115,274,309,386,239,200,336,188,199,181,181,116,311,229,290,663,239
%N A232894 Least positive integer m such that {Catalan(k) - k: k = 1, ..., m} contains a complete system of residues modulo n, or 0 if such a number m does not exist.
%C A232894 Conjecture: (i) Let n be any positive integer. Then 0 < a(n) <= n^2/2 + 7. Also, {Catalan(k) + k: k = 1, ..., [n^2/2] + 23} contains a complete system of residues modulo n, where [.] is the floor function.
%C A232894 (ii) For any integer n > 3, neither Catalan(n) - n nor Catalan(n) + n has the form x^m with m > 1 and x > 1.
%H A232894 Chai Wah Wu, <a href="/A232894/b232894.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..200 from Zhi-Wei Sun)
%e A232894 a(2) = 5 since Catalan(k) - k is even for each k = 1, 2, 3, 4, and Catalan(5) - 5 = 37 is odd.
%t A232894 L[m_,n_]:=Length[Union[Table[Mod[CatalanNumber[k]-k,n],{k,1,m}]]]
%t A232894 Do[Do[If[L[m,n]==n,Print[n," ",m];Goto[aa]],{m,1,n^2/2+7}];
%t A232894 Print[n," ",counterexample];Label[aa];Continue,{n,1,60}]
%Y A232894 Cf. A000108, A232616, A232862, A232898.
%K A232894 nonn
%O A232894 1,2
%A A232894 _Zhi-Wei Sun_, Dec 02 2013