A375584 a(n) = digit produced when the Michael Damm error-detecting algorithm is applied to n.

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

Offset: 1

Author

Darío Clavijo, Aug 19 2024

Keywords

• nonn
• base

Links

• H. Michael Damm, Totally anti-symmetric quasigroups for all orders n not equal to 2 or 6, Discrete Math., 307:6 (2007), 715-729.
• Wikipedia, Damm algorithm.

Crossrefs

Cf. A093018, A374967.

Programs

Python

t = [
    [0, 3, 1, 7, 5, 9, 8, 6, 4, 2],
    [7, 0, 9, 2, 1, 5, 4, 8, 6, 3],
    [4, 2, 0, 6, 8, 7, 1, 3, 5, 9],
    [1, 7, 5, 0, 9, 8, 3, 4, 2, 6],
    [6, 1, 2, 3, 0, 4, 5, 9, 7, 8],
    [3, 6, 7, 4, 2, 0, 9, 5, 8, 1],
    [5, 8, 6, 9, 7, 2, 0, 1, 3, 4],
    [8, 9, 4, 5, 3, 6, 2, 0, 1, 7],
    [9, 4, 3, 8, 6, 1, 7, 2, 0, 5],
    [2, 5, 8, 1, 4, 3, 6, 7, 9, 0]
]
def a(n):
    i = 0
    for d in str(n):
        i = t[i][int(d)]
    return i
print([a(n) for n in range(0, 88)])