A393160 a(n) is the largest possible integer Euclidean distance between two lattice points with coordinates in the interval 0..n.

0, 1, 2, 3, 5, 5, 6, 7, 10, 10, 10, 11, 15, 15, 15, 17, 20, 20, 20, 20, 25, 29, 29, 29, 30, 30, 30, 30, 35, 35, 35, 35, 40, 40, 40, 40, 45, 45, 45, 45, 50, 50, 58, 58, 58, 58, 58, 58, 60, 60, 60, 60, 65, 65, 65, 73, 73, 73, 73, 73, 75, 75, 75, 87, 87, 87, 87

Offset

0,3

Comments

In other words, a(n)^2 is the largest sum of two square numbers <= n^2.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, PARI program

Formula

a(n) = A393159(n, n).

Example

a(4) = 5 corresponds to the distance between, among others, the lattice points (0, 0) and (3, 4).

Prog

(PARI) \\ See Links section.
(Python)
from math import isqrt
def A393160(n):
    c, s = 0, {x**2 for x in range(isqrt(n**2<<1)+1)}
    for x in range(n+1):
        z = x**2+(m:=isqrt(max(0, c-x**2)))**2
        for y in range(m, x+1):
            if z>c and z in s:
                c = z
            z += (y<<1)+1
    return isqrt(c) # Chai Wah Wu, Feb 08 2026

Crossrefs

Cf. A393159.

Sequence in context: A373188 A067535 A076752 * A079114 A058189 A361676

Adjacent sequences: A393157 A393158 A393159 * A393161 A393162 A393163

Keyword

nonn

Author

Rémy Sigrist, Feb 03 2026

Status

approved