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

Author

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

Keywords

• cons
• nonn

Examples

			0.765366864730179543456919968060797733522689124971254082867601271255092067920...
		

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.

Crossrefs

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

Programs

Mathematica

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

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

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