A374967 a(n) is the Verhoeff check digit for n.

0, 5, 7, 6, 3, 8, 2, 0, 9, 1, 9, 3, 1, 2, 5, 0, 6, 8, 4, 7, 4, 5, 7, 6, 3, 8, 2, 0, 9, 1, 1, 7, 9, 8, 0, 5, 4, 2, 6, 3, 8, 2, 0, 1, 9, 4, 5, 7, 3, 6, 5, 4, 2, 3, 6, 1, 7, 9, 0, 8, 7, 1, 4, 0, 8, 3, 9, 6, 2, 5, 3, 9, 6, 5, 2, 7, 1, 4, 8, 0, 0, 6, 8, 7, 4, 9, 3, 1

Offset: 0

Author

Darío Clavijo, Jul 25 2024

Keywords

• nonn
• easy
• base

Comments

The Verhoeff checksum is a single-digit error-detecting code.

Links

• J. Verhoeff, Error Detecting Decimal Codes Mathematical Centre Tracts, 29.
• Wikipedia, Dihedral group.
• Wikipedia, Verhoeff algorithm.

Crossrefs

Cf. A093018.

Programs

Python

d_table = [
    [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],[1, 2, 3, 4, 0, 6, 7, 8, 9, 5],
    [2, 3, 4, 0, 1, 7, 8, 9, 5, 6],[3, 4, 0, 1, 2, 8, 9, 5, 6, 7],
    [4, 0, 1, 2, 3, 9, 5, 6, 7, 8],[5, 9, 8, 7, 6, 0, 4, 3, 2, 1],
    [6, 5, 9, 8, 7, 1, 0, 4, 3, 2],[7, 6, 5, 9, 8, 2, 1, 0, 4, 3],
    [8, 7, 6, 5, 9, 3, 2, 1, 0, 4],[9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
]
p_table = [
    [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],[1, 5, 7, 6, 2, 8, 3, 0, 9, 4],
    [5, 8, 0, 3, 7, 9, 6, 1, 4, 2],[8, 9, 1, 6, 0, 4, 3, 5, 2, 7],
    [9, 4, 5, 3, 1, 2, 6, 8, 7, 0],[4, 2, 8, 6, 5, 7, 3, 9, 0, 1],
    [2, 7, 9, 3, 8, 0, 6, 4, 1, 5],[7, 0, 4, 6, 9, 1, 3, 2, 5, 8]
]
j_table = [0, 4, 3, 2, 1, 5, 6, 7, 8, 9]
def a(n):
    c, ds = 0, list(map(int, str(n*10)[::-1]))
    for i, d in enumerate(ds):
        c = d_table[c][p_table[i % 8][d]]
    return j_table[c]
print([a(n) for n in range(0, 55)])