Fibonacciësque multiplicative sequences for prime moduli 2 through 29.
modulus 2 | |
---|---|
period | multiplicative sequence |
1 | [ 1 ] |
census: 1×1 = 1 = 1×1 |
modulus 3 | |
---|---|
period | multiplicative sequence |
1 | [ 1 ] |
3 | [ 1 2 2 ] |
census: 1×1 + 3×1 = 4 = 2×2 |
modulus 5 | |
---|---|
period | multiplicative sequence |
1 | [ 1 ] |
6 | [ 1 2 2 4 3 2 ] |
6 | [ 1 3 3 4 2 3 ] |
3 | [ 1 4 4 ] |
census: 1×1 + 3×1 + 6×2 = 16 = 4×4 |
modulus 7 | |
---|---|
period | multiplicative sequence |
1 | [ 1 ] |
8 | [ 1 2 2 4 1 4 4 2 ] |
24 | [ 1 3 3 2 6 5 2 3 6 4 3 5 1 5 5 4 6 3 4 5 6 2 5 3 ] |
3 | [ 1 6 6 ] |
census: 1×1 + 3×1 + 8×1 + 24×1 = 36 = 6×6 |
modulus 11 | |
---|---|
period | multiplicative sequence |
1 | [ 1 ] |
60 | [ 1 2 2 4 8 10 3 8 2 5 10 6 5 8 7 1 7 7 5 2 10 9 2 7 3 10 8 3 2 6 1 6 6 3 7 10 4 7 6 9 10 2 9 7 8 1 8 8 9 6 10 5 6 8 4 10 7 4 6 2 ] |
20 | [ 1 3 3 9 5 1 5 5 3 4 1 4 4 5 9 1 9 9 4 3 ] |
3 | [ 1 10 10 ] |
12 | [ 2 3 6 7 9 8 6 4 2 8 5 7 ] |
4 | [ 3 5 4 9 ] |
census: 1×1 + 3×1 + 4×1 + 12×1 + 20×1 + 60×1 = 100 = 10×10 |
modulus 13 | |
---|---|
period | multiplicative sequence |
1 | [ 1 ] |
24 | [ 1 2 2 4 8 6 9 2 5 10 11 6 1 6 6 10 8 2 3 6 5 4 7 2 ] |
8 | [ 1 3 3 9 1 9 9 3 ] |
24 | [ 1 4 4 3 12 10 3 4 12 9 4 10 1 10 10 9 12 4 9 10 12 3 10 4 ] |
6 | [ 1 5 5 12 8 5 ] |
24 | [ 1 7 7 10 5 11 3 7 8 4 6 11 1 11 11 4 5 7 9 11 8 10 2 7 ] |
6 | [ 1 8 8 12 5 8 ] |
3 | [ 1 12 12 ] |
24 | [ 2 6 12 7 6 3 5 2 10 7 5 9 6 2 12 11 2 9 5 6 4 11 5 3 ] |
24 | [ 2 8 3 11 7 12 6 7 3 8 11 10 6 8 9 7 11 12 2 11 9 8 7 4 ] |
census: 1×1 + 3×1 + 6×2 + 8×1 + 24×5 = 144 = 12×12 |
modulus 17 | |
---|---|
period | multiplicative sequence |
1 | [ 1 ] |
12 | [ 1 2 2 4 8 15 1 15 15 4 9 2 ] |
24 | [ 1 3 3 9 10 5 16 12 5 9 11 14 1 14 14 9 7 12 16 5 12 9 6 3 ] |
6 | [ 1 4 4 16 13 4 ] |
24 | [ 1 5 5 8 6 14 16 3 14 8 10 12 1 12 12 8 11 3 16 14 3 8 7 5 ] |
24 | [ 1 6 6 2 12 7 16 10 7 2 14 11 1 11 11 2 5 10 16 7 10 2 3 6 ] |
24 | [ 1 7 7 15 3 11 16 6 11 15 12 10 1 10 10 15 14 6 16 11 6 15 5 7 ] |
12 | [ 1 8 8 13 2 9 1 9 9 13 15 8 ] |
6 | [ 1 13 13 16 4 13 ] |
3 | [ 1 16 16 ] |
24 | [ 2 6 12 4 14 5 2 10 3 13 5 14 2 11 5 4 3 12 2 7 14 13 12 3 ] |
12 | [ 2 8 16 9 8 4 15 9 16 8 9 4 ] |
12 | [ 2 13 9 15 16 2 15 13 8 2 16 15 ] |
24 | [ 3 4 12 14 15 6 5 13 14 12 15 10 14 4 5 3 15 11 12 13 3 5 15 7 ] |
24 | [ 3 7 4 11 10 8 12 11 13 7 6 8 14 10 4 6 7 8 5 6 13 10 11 8 ] |
24 | [ 3 10 13 11 7 9 12 6 4 7 11 9 14 7 13 6 10 9 5 11 4 10 6 9 ] |
census: 1×1 + 3×1 + 6×2 + 12×4 + 24×8 = 256 = 16×16 |
modulus 19 | |
---|---|
period | multiplicative sequence |
1 | [ 1 ] |
24 | [ 1 2 2 4 8 13 9 3 8 5 2 10 1 10 10 5 12 3 17 13 12 4 10 2 ] |
24 | [ 1 3 3 9 8 15 6 14 8 17 3 13 1 13 13 17 12 14 16 15 12 9 13 3 ] |
24 | [ 1 4 4 16 7 17 5 9 7 6 4 5 1 5 5 6 11 9 4 17 11 16 5 4 ] |
24 | [ 1 6 6 17 7 5 16 4 7 9 6 16 1 16 16 9 11 4 6 5 11 17 16 6 ] |
8 | [ 1 7 7 11 1 11 11 7 ] |
24 | [ 1 8 8 7 18 12 7 8 18 11 8 12 1 12 12 11 18 8 11 12 18 7 12 8 ] |
24 | [ 1 9 9 5 7 16 17 6 7 4 9 17 1 17 17 4 11 6 9 16 11 5 17 9 ] |
24 | [ 1 14 14 6 8 10 4 2 8 16 14 15 1 15 15 16 12 2 5 10 12 6 15 14 ] |
3 | [ 1 18 18 ] |
24 | [ 2 3 6 18 13 6 2 12 5 3 15 7 10 13 16 18 3 16 10 8 4 13 14 11 ] |
24 | [ 2 6 12 15 9 2 18 17 2 15 11 13 10 16 8 14 17 10 18 9 10 14 7 3 ] |
24 | [ 2 7 14 3 4 12 10 6 3 18 16 3 10 11 15 13 5 8 2 16 13 18 6 13 ] |
24 | [ 2 9 18 10 9 14 12 16 2 13 7 15 10 17 18 2 17 15 8 6 10 3 11 14 ] |
24 | [ 2 11 3 14 4 18 15 4 3 12 17 14 10 7 13 15 5 18 14 5 13 8 9 15 ] |
24 | [ 2 14 9 12 13 4 14 18 5 14 13 11 10 15 17 8 3 5 15 18 4 15 3 7 ] |
census: 1×1 + 3×1 + 8×1 + 24×13 = 324 = 18×18 |
modulus 23 | |
---|---|
period | multiplicative sequence |
1 | [ 1 ] |
10 | [ 1 2 2 4 8 9 3 4 12 2 ] |
10 | [ 1 3 3 9 4 13 6 9 8 3 ] |
10 | [ 1 4 4 16 18 12 9 16 6 4 ] |
30 | [ 1 5 5 2 10 20 16 21 14 18 22 5 18 21 10 3 7 21 9 5 22 18 5 21 13 20 7 2 14 5 ] |
10 | [ 1 6 6 13 9 2 18 13 4 6 ] |
30 | [ 1 7 7 3 21 17 12 20 10 16 22 7 16 20 21 6 11 20 13 7 22 16 7 20 2 17 11 3 10 7 ] |
10 | [ 1 8 8 18 6 16 4 18 3 8 ] |
10 | [ 1 9 9 12 16 8 13 12 18 9 ] |
30 | [ 1 10 10 8 11 19 2 15 7 13 22 10 13 15 11 4 21 15 16 10 22 13 10 15 12 19 21 8 7 10 ] |
30 | [ 1 11 11 6 20 5 8 17 21 12 22 11 12 17 20 18 15 17 2 11 22 12 11 17 3 5 15 6 21 11 ] |
10 | [ 1 12 12 6 3 18 8 6 2 12 ] |
10 | [ 1 13 13 8 12 4 2 8 16 13 ] |
30 | [ 1 14 14 12 7 15 13 11 5 9 22 14 9 11 7 8 10 11 18 14 22 9 14 11 16 15 10 12 5 14 ] |
30 | [ 1 15 15 18 17 7 4 5 20 8 22 15 8 5 17 16 19 5 3 15 22 8 15 5 6 7 19 18 20 15 ] |
10 | [ 1 16 16 3 2 6 12 3 13 16 ] |
30 | [ 1 17 17 13 14 21 18 10 19 6 22 17 6 10 14 2 5 10 4 17 22 6 17 10 9 21 5 13 19 17 ] |
10 | [ 1 18 18 2 13 3 16 2 9 18 ] |
30 | [ 1 19 19 16 5 11 9 7 17 4 22 19 4 7 5 12 14 7 6 19 22 4 19 7 18 11 14 16 17 19 ] |
30 | [ 1 20 20 9 19 10 6 14 15 3 22 20 3 14 19 13 17 14 8 20 22 3 20 14 4 10 17 9 15 20 ] |
30 | [ 1 21 21 4 15 14 3 19 11 2 22 21 2 19 15 9 20 19 12 21 22 2 21 19 8 14 20 4 11 21 ] |
3 | [ 1 22 22 ] |
10 | [ 2 3 6 18 16 12 8 4 9 13 ] |
15 | [ 2 7 14 6 15 21 16 14 17 8 21 7 9 17 15 ] |
5 | [ 2 16 9 6 8 ] |
30 | [ 2 20 17 18 7 11 8 19 14 13 21 20 6 5 7 12 15 19 9 10 21 3 17 5 16 11 15 4 14 10 ] |
15 | [ 3 11 10 18 19 20 12 10 5 4 20 11 13 5 19 ] |
5 | [ 3 12 13 18 4 ] |
census: 1×1 + 3×1 + 5×2 + 10×11 + 15×2 + 30×11 = 484 = 22×22 |
modulus 29 | |
---|---|
period | multiplicative sequence |
1 | [ 1 ] |
48 | [ 1 2 2 4 8 3 24 14 17 6 15 3 16 19 14 5 12 2 24 19 21 22 27 14 1 14 14 22 18 19 23 2 17 5 27 19 20 3 2 6 12 14 23 3 11 4 15 2 ] |
48 | [ 1 3 3 9 27 11 7 19 17 4 10 11 23 21 19 22 12 3 7 21 2 13 26 19 1 19 19 13 15 21 25 3 17 22 26 21 24 11 3 4 12 19 25 11 14 9 10 3 ] |
48 | [ 1 4 4 16 6 9 25 22 28 7 22 9 24 13 22 25 28 4 25 13 6 20 4 22 1 22 22 20 5 13 7 4 28 25 4 13 23 9 4 7 28 22 7 9 5 16 22 4 ] |
48 | [ 1 5 5 25 9 22 24 6 28 23 6 22 16 4 6 24 28 5 24 4 9 7 5 6 1 6 6 7 13 4 23 5 28 24 5 4 20 22 5 23 28 6 23 22 13 25 6 5 ] |
16 | [ 1 7 7 20 24 16 7 25 1 25 25 16 23 20 25 7 ] |
48 | [ 1 8 8 6 19 27 20 18 12 13 11 27 7 15 18 9 17 8 20 15 10 5 21 18 1 18 18 5 3 15 16 8 12 9 21 15 25 27 8 13 17 18 16 27 26 6 11 8 ] |
48 | [ 1 9 9 23 4 5 20 13 28 16 13 5 7 6 13 20 28 9 20 6 4 24 9 13 1 13 13 24 22 6 16 9 28 20 9 6 25 5 9 16 28 13 16 5 22 23 13 9 ] |
48 | [ 1 10 10 13 14 8 25 26 12 22 3 8 24 18 26 4 17 10 25 18 15 9 19 26 1 26 26 9 2 18 7 10 12 4 19 18 23 8 10 22 17 26 7 8 27 13 3 10 ] |
48 | [ 1 11 11 5 26 14 16 21 17 9 8 14 25 2 21 13 12 11 16 2 3 6 18 21 1 21 21 6 10 2 20 11 17 13 18 2 7 14 11 9 12 21 20 14 19 5 8 11 ] |
6 | [ 1 12 12 28 17 12 ] |
48 | [ 1 15 15 22 11 10 23 27 12 5 2 10 20 26 27 6 17 15 23 26 18 4 14 27 1 27 27 4 21 26 24 15 12 6 14 26 16 10 15 5 17 27 24 10 8 22 2 15 ] |
16 | [ 1 16 16 24 7 23 16 20 1 20 20 23 25 24 20 16 ] |
6 | [ 1 17 17 28 12 17 ] |
16 | [ 1 23 23 7 16 25 23 24 1 24 24 25 20 7 24 23 ] |
3 | [ 1 28 28 ] |
48 | [ 2 5 10 21 7 2 14 28 15 14 7 11 19 6 27 17 24 2 19 9 26 2 23 17 14 6 26 11 25 14 2 28 27 2 25 21 3 5 15 17 23 14 3 13 10 14 24 17 ] |
48 | [ 2 8 16 12 18 13 2 26 23 18 8 28 21 8 23 10 27 9 11 12 16 18 27 22 14 18 20 12 8 9 14 10 24 8 18 28 11 18 24 26 15 13 21 12 20 8 15 4 ] |
48 | [ 2 9 18 17 16 11 2 22 15 11 20 17 21 9 15 19 24 21 11 28 18 11 24 3 14 13 8 17 20 21 14 4 27 21 16 17 11 13 27 3 23 11 21 28 8 21 23 19 ] |
48 | [ 2 11 22 10 17 25 19 11 6 8 19 7 17 3 22 8 2 16 3 19 28 10 19 16 14 21 4 26 17 7 3 21 5 18 3 25 17 19 4 18 14 20 19 3 28 26 3 20 ] |
48 | [ 2 12 24 27 10 9 3 27 23 12 15 6 3 18 25 15 27 28 2 27 25 8 26 5 14 12 23 15 26 13 19 15 24 12 27 5 19 8 7 27 15 28 14 15 7 18 10 6 ] |
48 | [ 3 12 7 26 8 5 11 26 25 12 10 4 11 15 20 10 26 28 3 26 20 27 18 22 19 12 25 10 18 6 21 10 7 12 26 22 21 27 16 26 10 28 19 10 16 15 8 4 ] |
census: 1×1 + 3×1 + 6×2 + 16×3 + 48×15 = 784 = 28×28 |