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

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, 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, 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

Offset: 0

Author

Robert G. Wilson v, Jul 18 2005

Keywords

• cofr
• nonn

Comments

Increasing PQ's: 1, 2, 24, 52, 132, 343, 664, 1329, 2136, ....

Examples

			1.7475645946331821906362... = 1 + 1/(1 + 1/(2 + 1/(1 + 1/(24 + ...)))). - _Harry J. Smith_, Apr 23 2009
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1793

Crossrefs

Cf. A085469 (decimal expansion).

Programs

Mathematica

ContinuedFraction[ 12Pi*Sum[ Sech[ Pi/2*Sqrt[(2j + 1)^2 + (2k + 1)^2]]^2, {j, 0, 36}, {k, 0, 36}], 98]

Extensions

Definition corrected by Leslie Glasser, Jan 24 2011

Definition corrected by Andrey Zabolotskiy, Jul 30 2020

Offset changed by Andrew Howroyd, Aug 09 2024