A396895 a(n) = 4*p - floor(2*sqrt(p))^2, where p = prime(n).

4, 3, 4, 3, 8, 3, 4, 12, 11, 16, 3, 4, 20, 3, 19, 16, 11, 19, 12, 28, 3, 27, 8, 32, 27, 4, 12, 28, 36, 11, 24, 40, 19, 27, 20, 28, 3, 27, 43, 16, 40, 48, 35, 43, 4, 12, 3, 51, 8, 16, 32, 56, 3, 43, 4, 28, 52, 60, 19, 35, 43, 16, 3, 19, 27, 43, 28, 52, 19, 27, 43, 67, 24, 48, 72

Offset

1,1

Comments

Sequences lists negated discriminants of the finite fields of prime order. Discriminants of finite fields are defined in the thesis of Zaitsev and the Alekseenko et al paper to study algebraic curves over finite fields.

Terms are congruent to 0, 3, 4 (mod 8). The indices n of d <= 20 are as follows, where p = prime(n):

- d = 3: p in A002383;

- d = 4: p in A002496;

- d = 8: p in A056899 \ {2,3};

- d = 11: p in A027753 \ {3,5};

- d = 12: p in A049423 \ {3,7};

- d = 16: p in A005473 \ {5,13};

- d = 19: p in A027755 \ {5,7,11,17};

- d = 20: p in A056905 \ {5}.

Links

Jianing Song, Table of n, a(n) for n = 1..10000

E. Alekseenko, S. Aleshnikov, N. Markin and A. Zaytsev, Optimal Curves of Genus 3 over Finite Fields with Discriminant -19, arXiv:0902.1901 [math.AG], 2009-2011. See Definition 1.1.

A.I. Zaitsev, Optimality properties of curves over finite fields, University of Armsterdam. See Section 3.1.

Mathematica

A396895[n_] := 4*# - Floor[2*Sqrt[#]]^2 & [Prime[n]];
Array[A396895, 100] (* Paolo Xausa, Jun 09 2026 *)

Prog

(PARI) a(n) = my(p=prime(n), r); sqrtint(4*p, &r); r

Crossrefs

Cf. A396869.

Cf. A002383, A002496, A056899, A027753, A049423, A005473, A027755, A056905.

Sequence in context: A241928 A111048 A016700 * A088910 A010308 A200625

Adjacent sequences: A396892 A396893 A396894 * A396896 A396897 A396898

Keyword

nonn,easy

Author

Jianing Song, Jun 09 2026

Status

approved