A091729 Norms of prime elements of Z[sqrt(-5)].

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

Offset: 1

Author

Paul Boddington, Feb 02 2004

Keywords

• easy
• nonn

Comments

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.

References

• 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.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A033205 (a subset), A033429, A038872.

The sequence of norms of prime ideals in the ring Z[sqrt(-5)] is A091727.

Programs

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

Extensions

a(43) corrected by Charles R Greathouse IV, Feb 09 2017