A392687 Decimal expansion of the average Euclidean distance between two randomly picked points, one of which is located in a unit square and the other in an adjacent unit square, both axis-parallel, with the two squares sharing one common vertex.

1, 4, 7, 3, 5, 6, 1, 5, 3, 2, 4, 3, 0, 5, 3, 6, 6, 9, 6, 2, 9, 0, 1, 1, 6, 4, 1, 6, 4, 8, 6, 2, 7, 0, 3, 0, 1, 2, 1, 0, 8, 1, 4, 3, 3, 7, 1, 3, 4, 1, 6, 1, 7, 4, 5, 4, 9, 9, 1, 2, 7, 1, 3, 1, 4, 7, 7, 4, 7, 7, 1, 6, 7, 0, 5, 9, 1, 3, 0, 9, 4, 7, 1, 0, 5, 4, 5, 6, 7, 5, 9

Offset

1,2

Links

Table of n, a(n) for n=1..91.

Formula

Equals 3*sqrt(2)/5 + sqrt(5)/3 - log(2)/12 - log(8) + 3*log(1+sqrt(2)) + (1/3)*log(7-3*sqrt(5)) + (61/24)*log(sqrt(5)-1) + (5/24)*log(sqrt(5)+1) - 1.

Equals 3*sqrt(2)/5 + sqrt(5)/3 - 1 + 3*log(1 + sqrt(2)) - 11*log((1 + sqrt(5))/2)/3. - Vaclav Kotesovec, Feb 18 2026

Example

1.47356153243053669629011641648627...

Mathematica

d[x1_, y1_, x2_, y2_] := Sqrt[(x1 - x2)^2 + (y1 - y2)^2]
N[Integrate[d[x1, y1, x2, y2], {x1, -1, 0}, {x2, 0, 1}, {y1, -1, 0}, {y2, 0, 1}], 100]

Prog

(PARI) 3*sqrt(2)/5 + sqrt(5)/3 - log(2)/12 - log(8) + 3*log(1+sqrt(2)) + (1/3)*log(7-3*sqrt(5)) + (61/24)*log(sqrt(5)-1) + (5/24)*log(sqrt(5)+1) - 1

Crossrefs

Cf. A135707.

Sequence in context: A241026 A198743 A271798 * A190357 A372861 A296499

Adjacent sequences: A392684 A392685 A392686 * A392688 A392689 A392690

Keyword

nonn,cons

Author

Hugo Pfoertner, Jan 20 2026

Status

approved