A395019 Decimal expansion of sqrt(105)/5 - 1.

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

Offset

1,3

Comments

The mode of the distribution of distances between two points in a unit ball. The probability density function is f(x) = 3*x^2 - 9*x^3/4 + 3*x^5/16, its mean is 36/35, and its median is A395020.

Links

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Ball Line Picking.

Index entries for algebraic numbers, degree 2.

Formula

Minimal polynomial: 5*x^2 + 10*x - 16.

Example

1.049390153191919676644207736104210398147006532690966...

Mathematica

RealDigits[Sqrt[105]/5 - 1, 10, 120][[1]]

Prog

(PARI) list(len) = my(c = 2*(quadgen(105)-3)/5); digits(floor(10^len * c));

Crossrefs

Cf. A093530, A093531, A176461, A394605 (disk), A394607 (square), A395018 (cube), A395020 (median).

Sequence in context: A329218 A373016 A359259 * A224953 A120869 A070436

Adjacent sequences: A395016 A395017 A395018 * A395020 A395021 A395022

Keyword

nonn,cons

Author

Amiram Eldar, Apr 10 2026

Status

approved