A347197 Decimal expansion of arccosh(phi) where phi is the golden ratio (1 + sqrt(5))/2.

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

Offset

1,3

Comments

This is the edge length of the {5,4} pentagonal tiling of the hyperbolic plane of curvature -1. This is also the edge length of both the (3,3,3,3,4,4) uniform tiling and the (3,3,3,4,3,4) uniform tiling of the hyperbolic plane of curvature -1.

Links

Table of n, a(n) for n=1..87.

Reddit user Marek14, The most interesting number in hyperbolic tilings.

Example

1.06127506190503565203301891621357348580678549893863...

Mathematica

RealDigits[ArcCosh[GoldenRatio], 10, 100][[1]] (* Amiram Eldar, Aug 23 2021 *)

Prog

(PARI) acosh((1+sqrt(5))/2) \\ Michel Marcus, Aug 23 2021

Crossrefs

Cf. A001622 (phi).

Sequence in context: A085766 A002329 A053453 * A156792 A021624 A021066

Adjacent sequences: A347194 A347195 A347196 * A347198 A347199 A347200

Keyword

nonn,cons

Author

Peter Kagey, Aug 22 2021

Status

approved