A232737 Decimal expansion of the real part of I^(1/8), or cos(Pi/16).

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

Offset: 0

Author

Stanislav Sykora, Nov 29 2013

Keywords

• nonn
• cons
• easy
• changed

Comments

The corresponding imaginary part is in A232738.

Examples

			0.9807852804032304491261822361342390369739337308933360950029160885453...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..1000
• Wikipedia, Trigonometric constants expressed in real radicals.
• Index entries for algebraic numbers, degree 8

Crossrefs

Cf. A232738 (imaginary part), A010503 (real(I^(1/2))), A010527 (real(I^(1/3))), A144981 (real(I^(1/4))), A019881 (real(I^(1/5))), A019884 (real(I^(1/6))), A232735 (real(I^(1/7))), A019889 (real(I^(1/9))), A019890 (real(I^(1/10))).

Programs

Mathematica

RealDigits[Cos[Pi/16], 10, 120][[1]] (* Amiram Eldar, Jun 29 2023 *)

PARI

real(I^(1/8)) \\ Seiichi Manyama, Apr 04 2021

PARI

cos(Pi/16) \\ Seiichi Manyama, Apr 04 2021

PARI

sqrt(2+sqrt(2+sqrt(2)))/2 \\ Seiichi Manyama, Apr 04 2021

Formula

Equals (1/2) * sqrt(2+sqrt(2+sqrt(2))). - Seiichi Manyama, Apr 04 2021

Root of 128*x^8 -256*x^6 +160*x^4 -32*x^2 +1 = 0. - R. J. Mathar, Aug 29 2025

2*this^2 -1 = A144981. - R. J. Mathar, Aug 29 2025

Equals 2F1(-1/8,1/8;1/2;1/2). - R. J. Mathar, Aug 31 2025