OFFSET
1,1
COMMENTS
Equivalently, integers k such that Z[sqrt(k)] = Z[x]/(x^2 - k) is a principal ideal domain.
-2, -1, together with k such that 4*k is in A003656.
All terms are squarefree and congruent to 2 or 3 modulo 4. It appears that the terms > 2 are of the form p or 2*p, where p is a prime congruent to 3 modulo 4. [This is correct; see Theorem 1 and Theorem 2 of Ezra Brown's link. - Jianing Song, Feb 24 2021]
The smallest prime p == 3 (mod 4) that is not a term is p = 79. The smallest prime p == 3 (mod 4) such that 2*p is not a term is p = 71.
LINKS
Jianing Song, Table of n, a(n) for n = 1..10000
Ezra Brown, Class numbers of real quadratic number fields, Trans. Amer. Math. Soc. 190 (1974), 99-107.
Mathematics Stack Exchange, Unique factorization domain that is not a Principal ideal domain
Eric Weisstein's World of Mathematics, Class Number
EXAMPLE
Z[sqrt(-1)] = Z[i] is the ring of Gaussian integers, which is a unique factorization domain.
PROG
(PARI) isA341649(n) = my(D=4*n); isfundamental(D) && quadclassunit(D)[1] == 1
CROSSREFS
KEYWORD
sign
AUTHOR
Jianing Song, Feb 16 2021
STATUS
approved