A139345 Decimal expansion of sine of the golden ratio. That is, the decimal expansion of sin((1+sqrt(5))/2).

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

Offset

0,1

Comments

By the Lindemann-Weierstrass theorem, this constant is transcendental. - Charles R Greathouse IV, May 13 2019

Links

Table of n, a(n) for n=0..103.

Mohammad K. Azarian, Problem 123, Missouri Journal of Mathematical Sciences, Vol. 10, No. 3 (Fall 1998), p. 176; Solution, ibid., Vol. 12, No. 1 (Winter 2000), pp. 61-62.

Index entries for transcendental numbers.

Formula

Equals sin(A001622).

Equals 1/A139350. - Amiram Eldar, Feb 07 2022

Example

0.99888450909488479883326824263012904463865119212705...

Mathematica

RealDigits[Sin[GoldenRatio], 10, 100][[1]] (* Amiram Eldar, Feb 07 2022 *)

Prog

(PARI) sin((1+sqrt(5))/2) \\ Charles R Greathouse IV, May 13 2019

Crossrefs

Cf. A001622, A094214, A104457, A098317, A002390, A139339, A139340, A139341, A139342, A139350.

Sequence in context: A019896 A175570 A050812 * A231470 A109942 A339745

Adjacent sequences: A139342 A139343 A139344 * A139346 A139347 A139348

Keyword

nonn,cons

Author

Mohammad K. Azarian, Apr 15 2008

Extensions

Leading zero removed by R. J. Mathar, Feb 05 2009

Status

approved