|
%I #14 Jul 20 2022 15:57:43
%S 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,
%T 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,
%U 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
%N Class number of Q(sqrt((-1)^((p-1)/2)*p)), where p = prime(n).
%C For n > 1, class number of the unique quadratic field with discriminant +-p, p = prime(n).
%C a(1) corresponds to Q(sqrt(2*i)) = Q(1+i) = Q(i).
%C All terms are odd.
%H Jianing Song, <a href="/A355879/b355879.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Class_number_(number_theory)#Class_numbers_of_quadratic_fields">Class numbers of quadratic fields</a>
%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%e prime(9) = 23, Q(sqrt(-23)) has class number 3, so a(9) = 3.
%e prime(15) = 47, Q(sqrt(-47)) has class number 5, so a(15) = 5.
%e prime(20) = 71, Q(sqrt(-71)) has class number 7, so a(20) = 7.
%e prime(50) = 229, Q(sqrt(229)) has class number 3, so a(50) = 3.
%o (PARI) a(n) = if(n==1, 1, my(p=prime(n)); qfbclassno(if(p%4==1, p, -p)))
%Y Cf. A002143, A002146.
%K nonn
%O 1,9
%A _Jianing Song_, Jul 20 2022
|
