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 A080216 #24 Jun 03 2025 05:25:13
%S A080216 0,1,1,1,1,3,3,4,2,5,5,7,7,7,11,8,8,9,9,13,16,11,11,15,15,13,21,18,18,
%T A080216 18,18,18,26,26,21,25,25,21,31,28,28,29,29,31,39,27,27,36,34,31,41,34,
%U A080216 34,45,45,36,46,46,46,43,43,41,51,40,48,52,52,52,56,44,44,52,52,57,61
%N A080216 a(n) is the largest value taken by binomial(n,j) mod j for j in [1..n].
%H A080216 Robin Visser, <a href="/A080216/b080216.txt">Table of n, a(n) for n = 1..10000</a>
%F A080216 a(n) = max_{j=1..n} binomial(n,j) mod j.
%e A080216 n=13: {binomial(13,j) mod j, j=1..13} = {0,0,1,3,2,0,1,7,4,6,1,1,1}; maximum is 7, so a(13) = 7.
%t A080216 Table[Max[Table[Mod[Binomial[n, j], j], {j, 1, n}]], {n, 1, 256}]
%o A080216 (PARI) a(n) = vecmax(vector(n, j, binomial(n, j) % j)); \\ _Michel Marcus_, Jul 29 2017
%o A080216 (Sage) def a(n):
%o A080216 return max([binomial(n,j)%j for j in range(1, n+1)]) # _Robin Visser_, Nov 26 2023
%Y A080216 Cf. A007318, A080217, A081370, A081371.
%K A080216 nonn
%O A080216 1,6
%A A080216 _Labos Elemer_, Mar 21 2003