A134976 Decimal expansion of (6 divided by golden ratio = 6/phi = 12/(1 + sqrt(5))).

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

Offset

1,1

Links

Table of n, a(n) for n=1..86.

Hideyuki Ohtsuka, Problem B-1373, Elementary problems and solutions, The Fibonacci Quarterly, Vol. 63, No. 4 (2025), p. 754.

Index entries for algebraic numbers, degree 2

Formula

Equals A010499 - 3. - R. J. Mathar, Apr 18 2008

From Amiram Eldar, Mar 18 2024: (Start)

Equals 2 * A134973.

Equals Product_{k>=0} (1 + 1/A192222(k)). (End)

From Amiram Eldar, Dec 16 2025: (Start)

Equals 3 + 3/phi^3, where phi is the golden ratio (A001622).

Equals 3 + Product_{k>=3} ((Fibonacci(k)^2+1)/(Fibonacci(k)^2-1))^((-1)^k) (Ohtsuka, 2025). (End)

Minimal polynomial x^2+6*x-36. - R. J. Mathar, Jun 03 2026

Example

3.708203932499...

Mathematica

RealDigits[6/GoldenRatio, 10, 120][[1]] (* Harvey P. Dale, Apr 29 2015 *)

Prog

(PARI) 12/(1+sqrt(5)) \\ Charles R Greathouse IV, Apr 05 2026

Crossrefs

Cf. A000045, A001622, A010499, A134973, A192222.

Sequence in context: A086729 A332527 A175576 * A192044 A010622 A103844

Adjacent sequences: A134973 A134974 A134975 * A134977 A134978 A134979

Keyword

cons,nonn

Author

Omar E. Pol, Nov 15 2007

Status

approved