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A108778 Continued fraction expansion of the Madelung constant for the face-centered cubic lattice (A085469). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1794

EXAMPLE

-M3=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]

PROG

(PARI) { default(realprecision, 1848); Madelung=-1.7475645946331821906362120355443974034851614366247417581\

5282535076504062353276117989075836269460788993083258153875371059328\

2029944183828013036933002156599363282376607172297568659238037167203\

8104106034214556064382777786832173132243697558773426250474787821285\

0860567916681675739924476841297036782518576281093713133720767071931\

9742497158115723096992309669273949657781107222671520547409011506891\

5716583082820050184892117803134673122964985828828184357133159143170\

0549563253348875363026704256274869484380028002592700268475574364975\

5049224613623992040015750630397214664811151237364010295066011939046\

7194373312530445102911514639759331918047977946099333746429426562908\

9693447792968854190440791425583272199718409067468023761538935445655\

0360273028544084934430280626704418241200439741867661772447563953444\

2306853849527943580751895490309305073843954464206438717926390780392\

0744282097957917736992304082214374645668043105692663197550459224432\

4807489408062474936107093630914922436898693314090379682324079004628\

4485812201497496519179081118204181820099174737652482957295684972796\

0238432587361742516304301213253823307779481444598420343673216212916\

2257903116101353527417534916776824438057139382407124829068734888254\

4125452570636795213611364128355999680725389089412120267587472631283\

4068262537606780890814341434286117388903537106985249308735988759660\

2363184706607516442145683455586623676605437844742512217481810852938\

2986359330038858941133489312302314299432802377837641811377123806642\

4808681158556451188180538368104068069306152452657895325624057864079\

5650016172016637963148270800941668173022273735813292616204948281860\

4313652035571121839219375759423906825690022886650812437760991098879\

3853419448765682333487553786009201932911164565934512096197118655146\

2827591256212354525900502281084479644187471007265894559896882147628\

71074726392395758480653025376082029590142679877534; x=contfrac(-Madelung); for (n=1, 1794, write("b108778.txt", n, " ", x[n])); } \\ Harry J. Smith, May 15 2009

CROSSREFS

Cf. A085469.

Sequence in context: A255861 A059360 A279308 * 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

STATUS

approved

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Last modified May 22 18:53 EDT 2019. Contains 323481 sequences. (Running on oeis4.)