A355879 Class number of Q(sqrt((-1)^((p-1)/2)*p)), where p = prime(n).

1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 5, 1, 3, 1, 1, 7, 1, 5, 3, 1, 1, 1, 5, 3, 1, 1, 5, 5, 1, 3, 1, 7, 1, 1, 11, 1, 5, 1, 13, 1, 1, 9, 3, 7, 5, 3, 1, 15, 1, 7, 3, 13, 1, 11, 1, 1, 3, 1, 3, 19, 1, 1, 3, 1, 5, 1, 1, 19, 9, 1, 3, 17, 1, 1, 5, 1, 9, 1, 21, 1, 15, 5, 1, 1, 1, 7

Offset: 1

Author

Jianing Song, Jul 20 2022

Keywords

• nonn

Comments

For n > 1, class number of the unique quadratic field with discriminant +-p, p = prime(n).

a(1) corresponds to Q(sqrt(2*i)) = Q(1+i) = Q(i).

All terms are odd.

Examples

			prime(9) = 23, Q(sqrt(-23)) has class number 3, so a(9) = 3.
prime(15) = 47, Q(sqrt(-47)) has class number 5, so a(15) = 5.
prime(20) = 71, Q(sqrt(-71)) has class number 7, so a(20) = 7.
prime(50) = 229, Q(sqrt(229)) has class number 3, so a(50) = 3.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..10000
• Wikipedia, Class numbers of quadratic fields
• Index entries for sequences related to quadratic fields

Crossrefs

Cf. A002143, A002146.

Programs

PARI

a(n) = if(n==1, 1, my(p=prime(n)); qfbclassno(if(p%4==1, p, -p)))