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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: A050877 A063203 A130244 this_sequence A130235 A129726 A122489

Adjacent sequences: A055022 A055023 A055024 this_sequence A055026 A055027 A055028

KEYWORD

nonn,easy,nice

AUTHOR

njas, Jun 09 2000

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Oct 03 2000

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Last modified September 6 16:04 EDT 2008. Contains 143483 sequences.


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