cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A330165 Odd terms in A003171: negated odd discriminants of orders of imaginary quadratic fields with 1 class per genus.

Original entry on oeis.org

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

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Author

Jianing Song, Dec 04 2019

Keywords

Comments

A003171 = 4*A000926 U {a(n)}.
Note that d is in A000926 (i.e., 4d is in A003171) if and only if: for all gcd(d,k) = 1, if k^2 < 3d, then d + k^2 is either a prime, or twice a prime, or the square of a prime, or 8 or 16. It seems that d is in this sequence if and only if: for all odd k, gcd(d,k) = 1, if k^2 < 3d, then (d + k^2)/4 is either a prime or the square of a prime.
It is conjectured that this is the full list. Otherwise, there could be at most one more term d such that -d is a fundamental discriminant.

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.
		

Crossrefs

Programs

  • PARI
    isA330165(n) = (n>0) && (n%4==3) && !#select(k->k<>2, quadclassunit(-n).cyc)