A355424 Positive integers m such that the real quadratic fields of the form Q(sqrt(m^2+4)) have class number 1.

1, 3, 5, 7, 13, 17

Offset

1,2

Comments

Former Yokoi's conjecture, proved by Biró in 2003 (see References). There are only six real quadratic fields of the form Q(sqrt(a(n)^2+4)), where Q indicates the set of rational numbers, with class number one.

Links

Table of n, a(n) for n=1..6.

A. Biró, Yokoi's conjecture, Acta Arith., vol. 106(1), 2003, pp. 85-104.

Formula

Let n be a positive integer less than 7. a(n) = 4*n - 7 iff n = 5, 6 and a(n) = 1 + 2*(n - 1) otherwise.

Example

a(1) = 1, since h(1^2 + 4) = h(5) = 1.

Crossrefs

Cf. A050950, A053329, A308420.

Sequence in context: A246026 A188574 A247458 * A339501 A008996 A261089

Adjacent sequences: A355421 A355422 A355423 * A355425 A355426 A355427

Keyword

nonn,fini,full

Author

Marco Ripà, Jul 01 2022

Status

approved