A330165 Odd terms in A003171: negated odd discriminants of orders of imaginary quadratic fields with 1 class per genus.
3, 7, 11, 15, 19, 27, 35, 43, 51, 67, 75, 91, 99, 115, 123, 147, 163, 187, 195, 235, 267, 315, 403, 427, 435, 483, 555, 595, 627, 715, 795, 1155, 1435, 1995, 3003, 3315
Offset: 1
Examples
For d = 315, (d + k^2)/4 can be 79, 109, 121, 151, 169, 211, 289, each is a prime or the square of a prime. For d = 3315 which is the largest known odd term in A003171, (d + k^2)/4 can be: 829, 841, 859, 919, 961, 1039, 1069, 1171, 1249, 1291, 1381, 1429, 1531, 1699, 1759, 1951, 2089, 2161, 2311, 2389, 2551, 2809, 3181, each is a prime or the square of a prime.
Links
- Günther Frei, Euler's convenient numbers, Math. Intell. Vol. 7 No. 3 (1985), 55-58 and 64.
- P. Weinberger, Exponents of the class groups of complex quadratic fields, Acta Arith., 22 (1973), 117-124.
Programs
-
PARI
isA330165(n) = (n>0) && (n%4==3) && !#select(k->k<>2, quadclassunit(-n).cyc)
Comments