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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 (list; constant; graph; refs; listen; history; text; internal format)
 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

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Last modified May 30 14:11 EDT 2023. Contains 363055 sequences. (Running on oeis4.)