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

0,3

Comments

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

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A085469 (decimal expansion).

Sequence in context: A368016 A279308 A345262 * A271530 A062763 A243147

Adjacent sequences: A108775 A108776 A108777 * A108779 A108780 A108781

Keyword

cofr,nonn

Author

Robert G. Wilson v, Jul 18 2005

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

Status

approved