A391672 Decimal expansion of sqrt(2+sqrt(2+sqrt(2))).

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

Offset

1,2

Comments

Algebraic integer of degree 8.

Largest 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 A391673, A391674 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(Pi/16) = 2*A232737.

Example

1.96157056080646089825236447226847807394786746178667...

Mathematica

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

Crossrefs

Cf. A187360, A272535, A391673, A391674.

Sequence in context: A176532 A178809 A021108 * A021840 A198582 A199082

Adjacent sequences: A391669 A391670 A391671 * A391673 A391674 A391675

Keyword

nonn,cons,easy

Author

A.H.M. Smeets, Dec 16 2025

Status

approved