cp's OEIS Frontend

A214726 Decimal expansion of the perimeter of Cairo and Prismatic tiles.

%I A214726 #46 Jul 14 2024 17:59:11
%S A214726 3,8,6,3,7,0,3,3,0,5,1,5,6,2,7,3,1,4,6,9,9,8,9,7,2,7,9,8,9,1,5,5,8,9,
%T A214726 4,7,0,5,3,5,6,1,9,3,5,6,0,3,3,6,1,8,2,0,1,6,0,9,3,7,2,3,0,5,2,4,1,6,
%U A214726 9,2,8,5,5,9,1,9,4,2,2,0,6,5,3,9,0,2,4,6,9,6,7,4,3,2,2,8,1,8,0,7,5,5
%N A214726 Decimal expansion of the perimeter of Cairo and Prismatic tiles.
%C A214726 An algebraic integer with degree 4 and minimal polynomial x^4 - 16x^2 + 16. - _Charles R Greathouse IV_, Apr 21 2016
%C A214726 Length of the longest diagonal in a regular 12-gon with unit side. - _Mohammed Yaseen_, Dec 13 2020
%H A214726 Paolo Xausa, <a href="/A214726/b214726.txt">Table of n, a(n) for n = 1..10000</a>
%H A214726 Ping Ngai Chung, Miguel A. Fernandez, Yifei Li, Michael Mara, Frank Morgan, Isamar Rosa Plata, Niralee Shah, Luis Sordo Vieira, and Elena Wikner, <a href="https://www.ams.org/journals/notices/201205/rtx120500632p.pdf">Isoperimetric Pentagonal Tilings</a>, Not. AMS, Vol. 59, No. 5 (May 2012) pp. 632-640; <a href="https://arxiv.org/abs/1111.6161">arXiv preprint</a>, arXiv:1111.6161 [math.MG], 2011.
%F A214726 Equals 2*(sqrt(2+sqrt(3))).
%F A214726 Equals csc(Pi/12). - _Amiram Eldar_, May 28 2021
%F A214726 Equals sqrt(2) + sqrt(6). - _Vaclav Kotesovec_, May 28 2021
%F A214726 Equals Product_{k>=1} (25 - 144*k^2)/(100 - 144*k^2). - _Antonio Graciá Llorente_, Jul 13 2024
%F A214726 Equals 4 * A019884. - _Alois P. Heinz_, Jul 14 2024
%e A214726 3.8637033051562731469989727989....
%t A214726 First[RealDigits[Csc[Pi/12],10,100]] (* _Paolo Xausa_, Oct 19 2023 *)
%o A214726 (PARI) 2*sqrt(2+sqrt(3)) \\ _Charles R Greathouse IV_, Apr 21 2016
%Y A214726 Cf. A002193, A002194, A019884.
%K A214726 nonn,cons,easy
%O A214726 1,1
%A A214726 _Jonathan Vos Post_, Jul 26 2012
%E A214726 a(100) corrected by _Georg Fischer_, Jul 12 2021