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A108778 Continued fraction expansion of the Madelung constant for the NaCl structure (A085469). 2

%I #18 Jul 30 2020 15:14:48

%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 = 1..1794</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.

%K cofr,nonn

%O 1,3

%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

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Last modified May 7 17:24 EDT 2024. Contains 372310 sequences. (Running on oeis4.)