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A091729 Norms of prime elements of Z[sqrt(-5)]. 4

%I #18 Feb 09 2017 11:17:47

%S 5,29,41,61,89,101,109,121,149,169,181,229,241,269,281,289,349,361,

%T 389,401,409,421,449,461,509,521,541,569,601,641,661,701,709,761,769,

%U 809,821,829,881,929,941,961,1009

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

%C 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.

%D David A. Cox, Primes of the form x^2+ny^2, Wiley, 1989.

%D A. Frohlich and M. J. Taylor, Algebraic number theory, Cambridge university press, 1991.

%H Charles R Greathouse IV, <a href="/A091729/b091729.txt">Table of n, a(n) for n = 1..10000</a>

%o (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

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

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

%K easy,nonn

%O 1,1

%A _Paul Boddington_, Feb 02 2004

%E a(43) corrected by _Charles R Greathouse IV_, Feb 09 2017

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