|
Search: id:A055025
|
|
|
| A055025 |
|
Norms of Gaussian primes. |
|
+0
11
|
|
| 2, 5, 9, 13, 17, 29, 37, 41, 49, 53, 61, 73, 89, 97, 101, 109, 113, 121, 137, 149, 157, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281, 293, 313, 317, 337, 349, 353, 361, 373, 389, 397, 401, 409, 421, 433, 449, 457, 461, 509, 521, 529, 541, 557, 569
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
These are the primes in the ring of integers a+bi, a and b rational integers, i = sqrt(-1).
|
|
REFERENCES
|
R. K. Guy, Unsolved Problems in Number Theory, A16.
L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, NY, 1910, see Chap. V.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..1000
Index entries for Gaussian integers and primes
|
|
FORMULA
|
Consists of 2; rational primes = 1 (mod 4) [A002144]; and squares of rational primes = 3 (mod 4) [A002145^2 ]
|
|
EXAMPLE
|
There are 8 Gaussian primes of norm 5, +-1+-2i and +-2+-i, but only two inequivalent ones (2+-i).
|
|
CROSSREFS
|
Cf. A055026-A055029, A055664-...
Sequence in context: A063203 A130244 A161569 this_sequence A130235 A129726 A122489
Adjacent sequences: A055022 A055023 A055024 this_sequence A055026 A055027 A055028
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Jun 09 2000
|
|
EXTENSIONS
|
More terms from Larry Reeves (larryr(AT)acm.org), Oct 03 2000
|
|
|
Search completed in 0.002 seconds
|
