%I #22 Aug 09 2024 15:11:44
%S 1,1,2,1,24,1,10,1,1,52,1,8,1,1,1,4,2,27,2,3,1,4,1,1,1,4,2,2,1,3,1,2,
%T 1,2,1,1,3,1,51,1,4,3,3,4,1,2,1,14,1,1,1,1,1,4,7,1,3,38,4,1,2,1,2,1,1,
%U 1,6,4,5,1,14,2,18,1,10,2,5,2,2,2,9,1,4,1,23,1,2,1,2,3,132,343,2,1,1,4,3,2
%N Continued fraction expansion of the Madelung constant for the NaCl structure (A085469).
%C Increasing PQ's: 1, 2, 24, 52, 132, 343, 664, 1329, 2136, ....
%H Harry J. Smith, <a href="/A108778/b108778.txt">Table of n, a(n) for n = 0..1793</a>
%e 1.7475645946331821906362... = 1 + 1/(1 + 1/(2 + 1/(1 + 1/(24 + ...)))). - _Harry J. Smith_, Apr 23 2009
%t ContinuedFraction[ 12Pi*Sum[ Sech[ Pi/2*Sqrt[(2j + 1)^2 + (2k + 1)^2]]^2, {j, 0, 36}, {k, 0, 36}], 98]
%Y Cf. A085469 (decimal expansion).
%K cofr,nonn
%O 0,3
%A _Robert G. Wilson v_, Jul 18 2005
%E Definition corrected by _Leslie Glasser_, Jan 24 2011
%E Definition corrected by _Andrey Zabolotskiy_, Jul 30 2020
%E Offset changed by _Andrew Howroyd_, Aug 09 2024
|