OFFSET
1,1
COMMENTS
The integers have the form z = a + b*sqrt(2), a and b rational integers. The norm of z is a^2 - 2*b^2, which may be negative.
REFERENCES
L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, NY, 1910, see Chap. VII.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
FORMULA
Consists of 2; rational primes = +-1 (mod 8); and squares of rational primes = +-3 (mod 8).
MATHEMATICA
maxNorm = 593; s1 = Select[Range[-1, maxNorm, 8], PrimeQ]; s2 = Select[Range[1, maxNorm, 8], PrimeQ]; s3 = Select[Range[-3, Sqrt[maxNorm], 8], PrimeQ]^2; s4 = Select[Range[3, Sqrt[maxNorm], 8], PrimeQ]^2; Union[{2}, s1, s2, s3, s4] (* Jean-François Alcover, Dec 07 2012, from formula *)
PROG
(PARI) is(n)=!!if(isprime(n), setsearch([1, 2, 7], n%8), issquare(n, &n) && isprime(n) && setsearch([3, 5], n%8)) \\ Charles R Greathouse IV, Sep 10 2016
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
N. J. A. Sloane, Jun 09 2000
EXTENSIONS
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 Franklin T. Adams-Watters, May 05 2006
STATUS
approved