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A204188 Decimal expansion of sqrt(5)/4. 0
5, 5, 9, 0, 1, 6, 9, 9, 4, 3, 7, 4, 9, 4, 7, 4, 2, 4, 1, 0, 2, 2, 9, 3, 4, 1, 7, 1, 8, 2, 8, 1, 9, 0, 5, 8, 8, 6, 0, 1, 5, 4, 5, 8, 9, 9, 0, 2, 8, 8, 1, 4, 3, 1, 0, 6, 7, 7, 2, 4, 3, 1, 1, 3, 5, 2, 6, 3, 0, 2, 3, 1, 4, 0, 9, 4, 5, 1, 2, 2, 4, 8, 5, 3, 6, 0, 3, 6, 0, 2, 0, 9, 4, 6, 9, 5, 5, 6, 8, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Equals product_{n=1..infinity} (1 - 1/A000032(2^n)).

Essentially the same as A019863 and A019827. - R. J. Mathar, Jan 16 2012

The value is the distance of the W point of the Wigner-Seitz cell of the body-centered cubic lattice (that is the Brioullin zone of the face-centered cubic lattice) to its four nearest neighbors. Let the points of the simple cubic lattice be at (1,0,0), (0,1,0), (1,0,0) etc and the point in the cube center at (1/2, 1/2, 1/2). Then W is at (0, 1/4, 1/2) [or any of the 24 symmetry related positions like (0, 3/4, 1/2), (0, 1/2, 1/4) etc.], and the four lattice points closest to W are at (-1/2, 1/2, 1/2), (0,0,0), (1/2, 1/2, 1/2) and (0,0,1). [R. J. Mathar, Aug 19 2013]

REFERENCES

Y. Tachiya, Transcendence of certain infinite products, J. Number Theory 125 (2007), 182-200.

LINKS

Table of n, a(n) for n=0..99.

J. Sondow, Evaluation of Tachiya's algebraic infinite products involving Fibonacci and Lucas numbers, Diophantine Analysis and Related Fields 2011 - AIP Conference Proceedings, vol. 1385, pp. 97-100.

Wikipedia, Brillouin zone

EXAMPLE

0.5590169943749474241022934171828190588601545899028814310677243113526302... = 10*A020837/2.

MAPLE

evalf(sqrt(5)/4) ;

CROSSREFS

Cf. A002163.

Sequence in context: A218333 A212533 A081287 * A019843 A046567 A199155

Adjacent sequences:  A204185 A204186 A204187 * A204189 A204190 A204191

KEYWORD

nonn,cons

AUTHOR

Jonathan Sondow, Jan 14 2012

STATUS

approved

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Last modified September 1 09:51 EDT 2014. Contains 246289 sequences.