A363701 Numbers k with the property that the character table of S_k contains a zero in every column.

0, 1, 5, 6, 8, 9, 10, 12, 14, 17, 21, 28, 30, 32, 34, 36, 37, 38

Offset

1,3

Comments

This sequence contains A363675 and A363676.

Links

Table of n, a(n) for n=1..18.

Prog

(Sage)
k=39 # Find integer sequence up to this value
S=set()
L=set()
for n in IntegerRange(0, k):
    G = SymmetricGroup(n)
    C = G.conjugacy_classes()
    c = len(C)
    N = G.character_table()
    for j in IntegerRange(1, c):
        if 0 not in N[:, j]:
                S.add(n)
                break
for n in IntegerRange(0, k):
    if n not in S:
        L.add(n)
print(L)

Crossrefs

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

Sequence in context: A057854 A033266 A355641 * A353193 A102408 A240564

Adjacent sequences: A363698 A363699 A363700 * A363702 A363703 A363704

Keyword

nonn,more,hard

Author

Diego Martin Duro, Jun 16 2023

Status

approved