

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
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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 WignerSeitz cell of the bodycentered cubic lattice (that is the Brioullin zone of the facecentered 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), 182200.


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. 97100.
Wikipedia, Brillouin zone


FORMULA

Equals sqrt(5)/4 = (1 + 2*phi)/4, with the golden section phi from A001622.
Equals 5*A020837.


EXAMPLE

0.5590169943749474241022934171828190588601545899028814310677243113526302...


MAPLE

evalf(sqrt(5)/4);


PROG

(PARI) sqrt(5)/4 \\ Charles R Greathouse IV, Apr 21 2016


CROSSREFS

Cf. A001622, 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



