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

0,2

Comments

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

Links

Table of n, a(n) for n=0..87.

Wikipedia, Dihedral group.

Wikipedia, Verhoeff algorithm.

Prog

(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)])

Crossrefs

Cf. A093018.

Sequence in context: A059249 A175294 A196615 * A305200 A198730 A318733

Adjacent sequences: A374964 A374965 A374966 * A374968 A374969 A374970

Keyword

nonn,easy,base

Author

Darío Clavijo, Jul 25 2024

Status

approved