A134974 Decimal expansion of 4*(-1 + phi) = 4*A094214, where the golden ratio phi = A001622.

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

Offset: 1

Author

Omar E. Pol, Nov 15 2007

Keywords

• cons
• nonn
• easy

Comments

This equals the dimensionless q-entropy (Tsallis entropy) of the set of 5 probabilities {p_i = 1/5, i = 1..5} for q = 1/2, which is S/k = -(1 - 5*(1/5)^(1/2))/(1 - 1/2) (k is the Boltzmann constant). See the Wikipedia link. - Wolfdieter Lang, Dec 06 2018

This constant - 2 = 2*sqrt(5) - 4 is the area of a regular pentagram formed by connecting the vertices of a unit-area regular pentagon. - Amiram Eldar, Nov 12 2021

Examples

			2.47213595499957939281834733746255247...
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..2000
• Wikipedia, Tsallis entropy.

Crossrefs

Cf. A001622, A010476, A020762, A094214, A134972.

Programs

Maple

evalf[100](8/(1+sqrt(5))); # Muniru A Asiru, Dec 19 2018

Mathematica

RealDigits[4/GoldenRatio,10,120][[1]] (* Harvey P. Dale, Oct 30 2016 *)

PARI

2*(sqrt(5)-1) \\ or: digits( % \1e-35). - M. F. Hasler, Dec 14 2018

Formula

Equals 4*(-1 + phi) = 4*A094214, where phi = A001622. This is an integer in the field Q(sqrt(5)).

Equals 4/phi = 8/(1 + sqrt(5)).

Equals 10*A020762-2 = A010476-2. - R. J. Mathar, Oct 27 2008

Equals 2*(sqrt(5) - 1) = 2*A134972. - M. F. Hasler, Dec 14 2018

Extensions

More terms from Harvey P. Dale, Oct 30 2016

Edited by Wolfdieter Lang, Dec 14 2018