A080216 - OEIS

%I #25 Sep 22 2025 16:00:41

%S 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 18,18,18,26,26,21,25,25,21,31,28,28,29,29,31,39,27,27,36,34,31,41,34,

%U 34,45,45,36,46,46,46,43,43,41,51,40,48,52,52,52,56,44,44,52,52,57,61

%N a(n) is the largest value taken by binomial(n,j) mod j for j in [1..n].

%H Robin Visser, <a href="/A080216/b080216.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = max_{j=1..n} binomial(n,j) mod j.

%e 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 Table[Max[Table[Mod[Binomial[n, j], j], {j, 1, n}]], {n, 1, 256}]

%o (PARI) a(n) = vecmax(vector(n, j, binomial(n, j) % j)); \\ _Michel Marcus_, Jul 29 2017

%o (SageMath) def a(n):

%o     return max([binomial(n,j)%j for j in range(1, n+1)])  # _Robin Visser_, Nov 26 2023

%Y Cf. A007318, A080217, A081370, A081371.

%K nonn

%O 1,6

%A _Labos Elemer_, Mar 21 2003