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

Author

Marco Ripà, Jul 01 2022

Keywords

• nonn
• fini
• full

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.

Examples

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

Links

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

Crossrefs

Cf. A050950, A053329, A308420.

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.