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A091729
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Norms of prime elements of Z[sqrt(-5)].
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4
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5, 29, 41, 61, 89, 101, 109, 121, 149, 169, 181, 229, 241, 269, 281, 289, 349, 361, 389, 401, 409, 421, 449, 461, 509, 521, 541, 569, 601, 641, 661, 701, 709, 761, 769, 809, 821, 829, 881, 929, 941, 961, 1009
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OFFSET
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1,1
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COMMENTS
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Consists of those primes congruent to 1, 5, 9 (mod 20) together with the squares of those primes congruent to -1, -3, -7, -9 (mod 20). Suppose n appears in this sequence. Then the number of prime elements of norm n is 2 if n is 5 or a square and 4 otherwise.
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REFERENCES
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David A. Cox, Primes of the form x^2+ny^2, Wiley, 1989.
A. Frohlich and M. J. Taylor, Algebraic number theory, Cambridge university press, 1991.
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LINKS
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PROG
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(PARI) list(lim)=my(v=List([5]), t); forprime(p=29, lim, t=p%20; if(t==1||t==9, listput(v, p))); forprime(p=11, sqrtint(lim\1), t=p%20; if(t==11||t==13||t==17||t==19, listput(v, p^2))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017
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CROSSREFS
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The sequence of norms of prime ideals in the ring Z[sqrt(-5)] is A091727.
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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