OFFSET
1,1
COMMENTS
The following lists the types of numbers which appear (p,q are distinct primes, congruences are mod 20 and the number in square brackets gives the number of irreducible elements of that norm counting a and -a only once): 4 [1]; 5 [1]; p==1,9 [2]; p^2 where p==-1,-3,-7,-9 [1]; 2p where p==3,7 [2]; p^2 where p==3,7 [3]; pq where p,q==3,7 [4].
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
Jianing Song, Table of n, a(n) for n = 1..10000
FORMULA
See A091731 for examples. - Jianing Song, Dec 08 2025
CROSSREFS
Cf. A139513 (primes decomposing in Q(sqrt(-5))), A003626 (primes remaining inert in Q(sqrt(-5))), A033205 ((p) is the product of two principal ideals), A106865 ((p) is the product of two non-principal ideals).
Other sequences related to factorizations in Z[sqrt(-5)]: A091727, A091728, A091729, A091731, A262828.
KEYWORD
easy,nonn
AUTHOR
Paul Boddington, Feb 02 2004
EXTENSIONS
Offset corrected by Jianing Song, Dec 08 2025
STATUS
approved