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

1,1

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

Links

Muniru A Asiru, Table of n, a(n) for n = 1..2000

Wikipedia, Tsallis entropy.

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

Example

2.47213595499957939281834733746255247...

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 *)

Prog

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

Crossrefs

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

Sequence in context: A202841 A247290 A246183 * A244262 A166531 A133292

Adjacent sequences: A134971 A134972 A134973 * A134975 A134976 A134977

Keyword

cons,nonn

Author

Omar E. Pol, Nov 15 2007

Extensions

More terms from Harvey P. Dale, Oct 30 2016

Edited by Wolfdieter Lang, Dec 14 2018

Status

approved