## FANDOM

2,766 Pages

Thanks to the patterns of division, we can combine them and transfinite ordinals.

mod 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
$1^{\omega}$ 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
$2^{\omega}$ 0 0 1, 2 0 1, 2, 3, 4 2, 4 1, 2, 4 0 6* 5* 8* 4, 8 12* 2, 4, 8 1, 2, 4, 8 0 8* 7* 18* 4, 8, 12, 16
$3^{\omega}$ 0 1 0 1, 3 1, 2, 3, 4 3 6* 1, 3 0 1, 3, 5, 9 5* 3, 9 1, 3, 9 6* 3, 6, 9, 12 1, 3, 9, 11 16* 9 18* 1, 3, 7, 9
$4^{\omega}$ 0 0 1 0 1, 4 4

1, 2, 4

0 1, 4, 7 4, 6 5* 4 6* 2, 4, 8 1, 4 0 1, 4, 13, 16 4, 10, 16 9* 4, 16
$5^{\omega}$ 0 1 1, 2 1 0 1, 5 6* 1, 5 6* 5 5* 1, 5 1, 5, 8, 12 6* 5, 10 1, 5, 9, 13 16* 6* 9* 5
$6^{\omega}$ 0 0 0 0 1 0 1, 6 0 0 6 10* 0 12 6, 8 6 0 16* 0 9* 16
$7^{\omega}$ 0 1 1 1, 3

1, 2, 3, 4

1 0 1, 7 1, 4, 7 1, 3, 7, 9 10* 1, 7 12* 12* 1, 4, 7, 13 1, 7 16* 1, 7, 13 1, 7, 11 1, 3, 7, 9
$8^{\omega}$ 0 0 1, 2 0 1, 2, 3, 4 2, 4 1 0 1, 8 2, 4, 6, 8 10* 4, 8 1, 5, 8, 12 8 1, 2, 4, 8 0 8* 8, 10 6* 4, 8, 12, 16
$9^{\omega}$ 0 1 0 1 1, 4 3 1, 2, 4 1 0 1, 9 5* 9 1, 3, 9 1, 9, 11 6, 9 1, 9 8* 9 9* 1, 9
$10^{\omega}$ 0 0 1 0 0 4 6* 0 1 0 1, 10 1, 9 6* 6* 10 0 16* 10 18* 0
$11^{\omega}$ 0 1 1, 2 1, 3 1 1, 5 1, 2, 4 1, 3 6* 1 0 1, 11 11* 1, 9, 11 1, 11 1, 3, 9, 11 16* 6* 1, 7, 11 1, 11
$12^{\omega}$ 0 0 0 0 1, 2, 3, 4 0 6* 0 0 5* 1 0 1, 12 6* 3, 6, 9, 12 0 16* 0 6* 4, 8, 12, 16
$13^{\omega}$ 0 1 1 1 1, 2, 3, 4 1 1, 6 1, 5 1, 4, 7 1, 3, 5, 9 8* 1 0 1, 13 1, 4, 7, 13 1, 5, 9, 13 1, 4, 13, 16 1, 7, 13 18* 1, 9, 13, 17
$14^{\omega}$ 0 0 1, 2 0 1, 4 2, 4 0 0 6* 4, 6 5* 4, 8 1 0 1, 14 0 16* 7* 18* 4, 16
$15^{\omega}$ 0 1 0 1, 3 0 3 1 1, 7 0 5 5* 3, 9 12* 1 0 1, 15 8* 9 18* 5, 15
$16^{\omega}$ 0 0 1 0 1 4 1, 2, 4 0 1, 4, 7 6 5* 4 1, 3, 9 2, 4, 8 1 0 1, 16 4, 10, 16 9* 16
$17^{\omega}$ 0 1 1, 2 1 1, 2, 3, 4 1, 5 6* 1 1, 8 1, 3, 5, 9 10* 1, 5 6* 6* 1, 2, 4, 8, 1 0 1, 17 9* 1, 9, 13, 17
$18^{\omega}$ 0 0 0 0 1, 2, 3, 4 0 1, 2, 4 0 0 2, 4, 6, 8 10* 0 1, 5, 8, 12 2, 4, 8 3, 6, 9, 12 0 1 0 1, 18 4, 8, 12, 16
$19^{\omega}$ 0 1 1 1, 3 1, 4 1 6* 1, 3 1 1, 9 10* 1, 7 12 6* 1, 4 1, 3, 9, 11 8* 1 0 1, 19
$20^{\omega}$ 0 0 1, 2 0 0 2, 4 1, 6 0 6* 0 5* 4, 8 12* 6, 8 5, 10 0 16* 7* 1 0
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