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Search: id:A055673
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| A055673 |
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Absolute values of norms of primes in ring of integers Z[sqrt(2)]. |
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+0
1
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| 2, 7, 9, 17, 23, 25, 31, 41, 47, 71, 73, 79, 89, 97, 103, 113, 121, 127, 137, 151, 167, 169, 191, 193, 199, 223, 233, 239, 241, 257, 263, 271, 281, 311, 313, 337, 353, 359, 361, 367, 383, 401, 409, 431, 433, 439, 449, 457, 463, 479, 487, 503, 521, 569, 577, 593
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The integers have the form z = a+bsqrt(2), a and b rational integers. The norm of z is a^2-2b^2, which may be negative.
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REFERENCES
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L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, NY, 1910, see Chap. VII.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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Consists of 2; rational primes = +-1 (mod 8); and squares of rational primes = +-3 (mod 8).
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CROSSREFS
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Cf. A055026-A055029, A055669-A055672.
Cf. A118916, A118917.
Sequence in context: A042807 A005988 A079326 this_sequence A020895 A065139 A093916
Adjacent sequences: A055670 A055671 A055672 this_sequence A055674 A055675 A055676
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas, Jun 09 2000
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EXTENSIONS
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I would also like to get the sequences (analogous to A055027 and A055029) giving the number of inequivalent primes mod units. Of course now there are infinitely many units.
More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 05 2006
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