OFFSET
1,1
COMMENTS
Every element d of the sequence is squarefree because, if f is the squarefree part of d, then Q(sqrt(f)) = Q(sqrt(d)). If f would be < d, the class number of Q(sqrt(f)) would not be < the class number of Q(sqrt(d)). Thus, f = d.
REFERENCES
Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966.
LINKS
Robin Visser, Table of n, a(n) for n = 1..50
EXAMPLE
The sequence starts with 10 because the class number of Q(sqrt(10)) = 2 and all fields Q(sqrt(m)) with m < 10 have class number 1.
The next term is 79 because the class number of Q(sqrt(79)) is 3 and all fields Q(sqrt(m)) with m < 79 have class number 1 or 2.
MATHEMATICA
A={}; hx = 1; d = 2; While[hx<300, d++; If[SquareFreeQ[d], h = NumberFieldClassNumber[Sqrt[d]]; If[h > hx, AppendTo[A, d]; hx = h]]]; A
PROG
(PARI) classn(n) = qfbclassno(if(n%4>1, 4, 1)*n);
isok(d) = {if (issquarefree(d), cld = classn(d); for (k=2, d-1, if (issquarefree(k) && (classn(k) >= cld), return (0))); 1; ); } \\ Michel Marcus, Mar 13 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Emmanuel Vantieghem, Mar 13 2017
EXTENSIONS
More terms from Robin Visser, May 25 2024
STATUS
approved