A386241 Decimal expansion of sqrt(5)*sin(Pi/8).

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

Offset

0,1

Comments

Upper bound of the wobbling distance S of two rotated square lattices. See A307110 and A307731 for the special case of rotation angle Pi/4. According to Jan Fricke (1999), the angle Pi/4 is the most unfavorable case, i.e., smaller bounds can be found for all other angles.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Hans-Georg Carstens, Walter A. Deuber, Wolfgang Thumser, and Elke Koppenrade, Geometrical Bijections in Discrete Lattices. Combinatorics, Probability and Computing, 8(1-2), 109-129, 1999.

Jan Fricke, Symmetric Graphs have symmetric Matchings, arXiv:1607.07426 [math.GR], 25 Jul 2016, Introduction.

Klaus Nagel, A Lower Bound for Double Lattice Bijections, August 17, 2025.

Index entries for algebraic numbers, degree 4

Formula

Equals A002163*A182168.

The minimal polynomial is 8*x^4 - 40*x^2 + 25. - Joerg Arndt, Aug 02 2025

Example

0.8557061686312838477748180718246837073...

Mathematica

First[RealDigits[Sqrt[5]*Sin[Pi/8], 10, 100]] (* Paolo Xausa, Aug 13 2025 *)

Prog

(PARI) sqrt(5)*sin(Pi/8) \\ Charles R Greathouse IV, Aug 19 2025

Crossrefs

Cf. A002163, A144981, A182168, A307110, A307731, A367150.

Sequence in context: A393965 A011107 A356805 * A318335 A243379 A214174

Adjacent sequences: A386238 A386239 A386240 * A386242 A386243 A386244

Keyword

nonn,cons

Author

Hugo Pfoertner, Jul 18 2025

Status

approved