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

1,2

Links

Table of n, a(n) for n=1..88.

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.

Prog

(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)])

Crossrefs

Cf. A093018, A374967.

Sequence in context: A138257 A283975 A071043 * A101624 A166519 A213043

Adjacent sequences: A375581 A375582 A375583 * A375585 A375586 A375587

Keyword

nonn,base

Author

Darío Clavijo, Aug 19 2024

Status

approved