A391674 Decimal expansion of sqrt(2-sqrt(2-sqrt(2))).

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

Offset

1,6

Comments

Algebraic integer of degree 8.

Second smallest positive real root of x^8 - 8*x^6 + 20*x^4 - 16*x^2 + 2 = 0. The eight roots are s2*sqrt(2+s1*sqrt(2+s0*sqrt(2))), where s2, s1, s0 in {-1, 1} (see also A391672, A391673 and A272535).

Links

Table of n, a(n) for n=1..88.

Wolfdieter Lang, Minimal Polynomials of 2*cos(Pi/n)

Index entries for algebraic numbers, degree 8

Formula

Equals 2*cos(5*Pi/16).

Example

1.111140466039204449485661627897065748749874381509608...

Mathematica

RealDigits[Sqrt[2-Sqrt[2-Sqrt[2]]], 10, 88][[1]] (* Stefano Spezia, Dec 17 2025 *)

Crossrefs

Cf. A187360, A272535, A391672, A391673.

Sequence in context: A361620 A303560 A341481 * A135011 A184907 A127751

Adjacent sequences: A391671 A391672 A391673 * A391675 A391676 A391677

Keyword

nonn,cons,easy

Author

A.H.M. Smeets, Dec 16 2025

Status

approved