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%I #17 Jan 05 2025 19:51:38
%S 5,3,9,3,4,4,6,6,2,9,1,6,6,3,1,6,1,6,0,6,8,1,9,5,6,1,1,4,5,5,2,1,2,7,
%T 0,5,9,0,6,7,6,9,7,2,6,6,0,1,9,2,0,9,5,4,0,4,5,1,4,9,5,4,0,9,0,1,7,5,
%U 3,4,8,7,6,0,6,3,0,0,8,1,6,5,6,9,0,6,9,0,6,8,0,6,3,1,3,0,3,7,9,1,6,1,5,8,4,6,9,6,0,2,5,1,2,8,9,6,3,9,1,7
%N Decimal expansion of (golden ratio divided by 3 = phi/3 = (1 + sqrt(5))/6).
%C The vertex-to-face edge-length ratio between a dodecahedron and its enclosing dual icosahedron. See Wassell and Benito. - _Michel Marcus_, Sep 30 2019
%H Stephen R. Wassell and Samantha Benito, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/50-2/WassellBenito.pdf">Edge-Length Ratios Between Dual Platonic Solids: A Surprisingly New Result Involving the Golden Ratio</a>, Fib. Q. 50(2), 2012, 144-154.
%F Equals sqrt((3+sqrt(5))/18) or sqrt(6+2*sqrt(5))/6. See Wassell and Benito. - _Michel Marcus_, Sep 30 2019
%F Equals Product_{k>=2} (1 - 1/Fibonacci(2*k)). - _Amiram Eldar_, May 27 2021
%e 0.5393446629166...
%t RealDigits[GoldenRatio/3,10,120][[1]] (* _Harvey P. Dale_, Jan 15 2012 *)
%o (PARI) (1+sqrt(5))/6 \\ _Michel Marcus_, Sep 30 2019
%Y Cf. A000045, A001622 (phi).
%K cons,nonn,changed
%O 0,1
%A _Omar E. Pol_, Nov 15 2007
%E More terms from _Harvey P. Dale_, Jan 15 2012