A374001 a(n) is the number of elements z of Z_p[i] such that #{z^k, k >= 0} = p^2-1 (where p denotes A002145(n), the n-th prime number congruent to 3 modulo 4).
4, 16, 32, 96, 160, 256, 480, 704, 896, 1280, 1152, 1536, 1920, 3072, 3744, 4608, 3840, 4224, 5760, 8640, 7872, 8448, 9216, 9600, 9984, 13824, 16128, 12288, 14400, 20800, 18432, 25760, 23040, 23040, 26240, 38528, 34176, 42240, 31104, 48640, 34560, 48384, 46080
Offset: 1
Keywords
Examples
For n = 2:
- the second prime number congruent to 3 modulo 4 is p = 7,
- the number of elements of {(x + i*y)^k, k >= 0} where x and y belong to Z_7 are:
x\y | 0 1 2 3 4 5 6
----+--------------------------
0 | 2 4 12 12 12 12 4
1 | 1 24 48 48 48 48 24
2 | 3 48 8 16 16 8 48
3 | 6 48 16 24 24 16 48
4 | 3 48 16 24 24 16 48
5 | 6 48 8 16 16 8 48
6 | 2 24 48 48 48 48 24
- the number 48 appears 16 times, so a(2) = 16.
Links
- Rémy Sigrist, Scatterplot of (x, y) such that #{(x+i*y)^k, k >= 0} = p^2-1 (with p = A002145(62) = 647)
- Rémy Sigrist, C++ program
- StackExchange, Z_p[i] is a field?
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