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

%I A134974 #33 Sep 25 2024 09:25:11
%S A134974 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,
%T A134974 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,
%U A134974 4,1,8,5,1,2,7,5,6,0,9,7,9,8,8,2,8,8
%N A134974 Decimal expansion of 4*(-1 + phi) = 4*A094214, where the golden ratio phi = A001622.
%C A134974 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
%C A134974 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
%H A134974 Muniru A Asiru, <a href="/A134974/b134974.txt">Table of n, a(n) for n = 1..2000</a>
%H A134974 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tsallis_entropy">Tsallis entropy</a>.
%F A134974 Equals 4*(-1 + phi) = 4*A094214, where phi = A001622. This is an integer in the field Q(sqrt(5)).
%F A134974 Equals 4/phi = 8/(1 + sqrt(5)).
%F A134974 Equals 10*A020762-2 = A010476-2. - _R. J. Mathar_, Oct 27 2008
%F A134974 Equals 2*(sqrt(5) - 1) = 2*A134972. - _M. F. Hasler_, Dec 14 2018
%e A134974 2.47213595499957939281834733746255247...
%p A134974 evalf[100](8/(1+sqrt(5))); # _Muniru A Asiru_, Dec 19 2018
%t A134974 RealDigits[4/GoldenRatio,10,120][[1]] (* _Harvey P. Dale_, Oct 30 2016 *)
%o A134974 (PARI) 2*(sqrt(5)-1) \\ or: digits( % \1e-35). - _M. F. Hasler_, Dec 14 2018
%Y A134974 Cf. A001622, A010476, A020762, A094214, A134972.
%K A134974 cons,nonn,easy
%O A134974 1,1
%A A134974 _Omar E. Pol_, Nov 15 2007
%E A134974 More terms from _Harvey P. Dale_, Oct 30 2016
%E A134974 Edited by _Wolfdieter Lang_, Dec 14 2018