A139350 -id:A139350 - cp's OEIS frontend

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

Mohammad K. Azarian, Apr 15 2008

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

			0.99888450909488479883326824263012904463865119212705...

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.

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

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

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

Equals sin(A001622).

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

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

A140232 a(n) = ceiling(n*exp((1+sqrt(5))/2)).

Original entry on oeis.org

6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96, 101, 106, 111, 116, 122, 127, 132, 137, 142, 147, 152, 157, 162, 167, 172, 177, 182, 187, 192, 197, 202, 207, 212, 217, 222, 227, 232, 238, 243, 248, 253, 258, 263, 268, 273, 278, 283

Offset: 1

Mohammad K. Azarian, May 13 2008

nonn

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A001622, A094214, A104457, A098317, A002390, A139339, A139340, A139341, A139342, A139345, A139346, A139347, A139348, A139349, A139350, A140231, A016861.

phi:=(1+Sqrt(5))/2; [Ceiling(n*Exp(phi)): n in [1..60]]; // G. C. Greubel, Jun 30 2019

Ceiling[Exp[GoldenRatio]*Range[60]] (* G. C. Greubel, Jun 30 2019 *)

phi=(1+sqrt(5))/2; vector(60, n, ceil(n*exp(phi)) ) \\ G. C. Greubel, Jun 30 2019

[ceil(n*exp(golden_ratio)) for n in (1..60)] # G. C. Greubel, Jun 30 2019

a(n) = ceiling(n*A139341). - R. J. Mathar, Feb 06 2009

cp's OEIS Frontend

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

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