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