A101464 Decimal expansion of sqrt(2-sqrt(2)), edge length of a regular octagon with circumradius 1.

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

Offset

0,1

Comments

This is an algebraic integer, with its minimal polynomial being x^4 - 4*x^2 + 2 = 0. - A.H.M. Smeets, Nov 30 2025

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Eric Weisstein's World of Mathematics, Octagon.

Index entries for algebraic numbers, degree 4.

Formula

Equals i^(3/4) + i^(-3/4). - Gary W. Adamson, Jul 07 2022

Equals 2*sin(Pi/8) = 2*A182168. - Amiram Eldar, Apr 06 2023

Equals Product_ {k >= 0} ((8*k - 2)*(8*k + 10))/((8*k - 5)*(8*k + 13)). - Antonio Graciá Llorente, Mar 11 2024

Equals Product_{k>=1} (1 + (-1)^k/A047621(k)). - Amiram Eldar, Nov 22 2024

Equals sqrt(A101465) = 1/A285871 = exp(-A329246). - Hugo Pfoertner, Nov 22 2024

Example

0.765366864730179543456919968060797733522689124971254082867601271255092067920...

Mathematica

RealDigits[Sqrt[2-Sqrt[2]], 10, 120][[1]] (* Harvey P. Dale, Jun 22 2011 *)

Prog

(PARI) 2*sin(Pi/8) \\ Charles R Greathouse IV, Feb 04 2025
(PARI) polrootsreal(x^4-4*x^2+2)[3] \\ Charles R Greathouse IV, Feb 04 2025

Crossrefs

Cf. A047621, A101465, A179260 (sqrt(2+sqrt(2))), A182168, A285871, A329246.

Sequence in context: A372951 A334380 A395793 * A072558 A022963 A023449

Adjacent sequences: A101461 A101462 A101463 * A101465 A101466 A101467

Keyword

cons,nonn

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jan 20 2005

Status

approved