A392573 Decimal expansion of 4*Pi*arccot(sqrt(phi)), where phi is the golden ratio (A001622).

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

Offset

1,1

Comments

This is the solution given by Cleo (a pseudonym, which turned out to be Vladimir Reshetnikov) to the integral (see Formula section) appearing in question 562694 on Mathematics Stack Exchange (2013).

The solution was later confirmed by Ron Gordon, who provided a full proof.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Ron Gordon, Answer to question 562694, Mathematics Stack Exchange, 2013.

snus, Who is Cleo? | Math Internet Mystery [solved], YouTube video, 2026.

Wikipedia, Cleo (mathematician).

Formula

Equals Integral_{x = -1..1} sqrt((1 + x)/(1 - x))*log((2*x^2 + 2*x + 1)/(2*x^2 - 2*x + 1))/x dx.

Equals 4*A000796*A175288.

Example

8.3722116266012756616257471210984126380817280538822...

Mathematica

First[RealDigits[4*Pi*ArcCot[Sqrt[GoldenRatio]], 10, 100]]

Crossrefs

Cf. A000796, A001622, A175288.

Sequence in context: A372857 A277775 A199719 * A396024 A301813 A206161

Adjacent sequences: A392570 A392571 A392572 * A392574 A392575 A392576

Keyword

nonn,cons,easy

Author

Paolo Xausa, Feb 14 2026

Status

approved