A363701 - OEIS

%I #34 Nov 17 2024 07:31:37

%S 0,1,5,6,8,9,10,12,14,17,21,28,30,32,34,36,37

%N Numbers k with the property that the character table of S_k contains a zero in every nontrivial column.

%C This sequence contains A363675 and A363676.

%o (Sage)

%o def zeros(n):

%o     G = SymmetricGroup(n)

%o     N = G.character_table()

%o     for j in range(1,N.ncols()):

%o         if 0 not in N[:,j]:

%o             return False

%o         j+=1

%o     return True

%o n=1

%o while n>0:

%o     if zeros(n) == True:

%o         print(n)

%o     n+=1

%Y Cf. A000217, A010054, A175595, A260682, A363675, A363676.

%K nonn,more,hard

%O 1,3

%A _Diego Martin Duro_, Jun 16 2023