A019889 -id:A019889 - cp's OEIS frontend

A019978 Decimal expansion of tangent of 80 degrees.

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

Offset: 1

N. J. A. Sloane

			tan(4*Pi/9) = 5.67128183...

Ivan Panchenko, Table of n, a(n) for n = 1..1000
Index entries for algebraic numbers, degree 6

RealDigits[Tan[80 Degree],10,120][[1]] (* Harvey P. Dale, Jan 04 2013 *)

Largest positive of the 6 real-valued roots of x^6-33*x^4+27*x^2-3=0. - R. J. Mathar, Aug 31 2025

Equals A019889/A019819. - R. J. Mathar, Aug 31 2025

A343056 Decimal expansion of the real part of i^(1/16), or cos(Pi/32).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Apr 04 2021

			0.9951847266721968862448369...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Leon D. Fairbanks, Powers of Cosine and Sine, arXiv:2308.04437 [math.GM], 2023. See p. 3.
Wikipedia, Trigonometric constants expressed in real radicals.
Index entries for algebraic numbers, degree 16

cos(Pi/m): A010503 (m=4), A019863 (m=5), A010527 (m=6), A073052 (m=7), A144981 (m=8), A019879 (m=9), A019881 (m=10), A019884 (m=12), A232735 (m=14), A019887 (m=15), A232737 (m=16), A210649 (m=17), A019889 (m=18), A019890 (m=20), A144982 (m=24), A019893 (m=30). this sequence (m=32), A019894 (m=36).

R:= RealField(127); Cos(Pi(R)/32); // G. C. Greubel, Sep 30 2022

RealDigits[Cos[Pi/32], 10, 100][[1]] (* Amiram Eldar, Apr 27 2021 *)

PARI
```
real(I^(1/16))
```
PARI
```
cos(Pi/32)
```
PARI
```
sqrt(2+sqrt(2+sqrt(2+sqrt(2))))/2
```

numerical_approx(cos(pi/32), digits=122) # G. C. Greubel, Sep 30 2022

Equals (1/2) * sqrt(2+sqrt(2+sqrt(2+sqrt(2)))).
Satisfies 32768*x^16 -131072*x^14 +212992*x^12 -180224*x^10 +84480*x^8 -21504*x^6 +2688*x^4 -128*x^2 +1 = 0. - R. J. Mathar, Aug 29 2025
Equals 2F1(-1/16,1/16;1/2;1/2). - R. J. Mathar, Aug 31 2025

A383759 Decimal expansion of infinite nested radical sqrt(8-sqrt(8-sqrt(8+sqrt(8-...)))).

Original entry on oeis.org

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

Offset: 1

Artur Jasinski, May 09 2025

Sequence of signs is cyclic +,-,-,+,-,-,+,-,-,+,....

			2.41147412780977283851...

Bruce C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, 1994, Chapter 22, p. 19, eq. (5.11).

Cf. A019889.

RealDigits[Root[-17 - 6 x + 3 x^2 + x^3, 3], 10, 105][[1]]

Equals 2*sqrt(3)*cos(Pi/18) - 1.

Equals real root of cubic polynomial x^3 + 3*x^2 - 6*x - 17.

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A019978 Decimal expansion of tangent of 80 degrees.

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A343056 Decimal expansion of the real part of i^(1/16), or cos(Pi/32).

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A383759 Decimal expansion of infinite nested radical sqrt(8-sqrt(8-sqrt(8+sqrt(8-...)))).

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