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 A178959 Decimal expansion of the site percolation threshold for the (3,6,3,6) Kagome Archimedean lattice. 0

%I

%S 6,5,2,7,0,3,6,4,4,6,6,6,1,3,9,3,0,2,2,9,6,5,6,6,7,4,6,4,6,1,3,7,0,4,

%T 0,7,9,9,9,2,4,8,6,4,5,6,3,1,8,6,1,2,2,5,5,2,7,5,1,7,2,4,3,7,3,5,8,6,

%U 8,3,5,5,7,2,1,9,7,0,5,2,9,1,5,6,9,6,6,7,7,3,6,8,5,2,0,0,8,5,2

%N Decimal expansion of the site percolation threshold for the (3,6,3,6) Kagome Archimedean lattice.

%C Consider an infinite graph where vertices are selected with probability p. The site percolation threshold is a unique value p_c such that if p > p_c an infinite connected component of selected vertices will almost surely exist, and if p < p_c an infinite connected component will almost surely not exist. This sequence gives p_c for the (3,6,3,6) Kagome Archimedean lattice.

%D Sykes, M. F.; J. W. Essam (1964). "Exact critical percolation probabilities for site and bond problems in two dimensions". Journal of Mathematical Physics (N.Y.) 5 (8): 1117-1127. Bibcode 1964JMP.....5.1117S. doi:10.1063/1.1704215.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Percolation_threshold">Percolation threshold</a>

%F 1 - 2*sin(Pi/18).

%e 0.6527036446661393...

%t RealDigits[1 - 2 Sin[Pi/18], 10, 105][[1]] (* _Alonso del Arte_, Dec 22 2012 *)

%o (PARI) 1-2*sin(Pi/18) \\ _Charles R Greathouse IV_, Jan 03 2013

%Y Cf. A174849.

%K nonn,cons,easy

%O 0,1

%A _Jonathan Vos Post_, Dec 22 2012

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Last modified June 5 06:41 EDT 2020. Contains 334828 sequences. (Running on oeis4.)