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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} (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 LINKS 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. Y. Tachiya, Transcendence of certain infinite products, J. Number Theory 125 (2007), 182-200. 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); MATHEMATICA RealDigits[Sqrt[5]/4, 10, 100][[1]] (* Amiram Eldar, Dec 04 2018 *) PROG (PARI) sqrt(5)/4 \\ Charles R Greathouse IV, Apr 21 2016 CROSSREFS Cf. A001622, A002163. Sequence in context: A212533 A081287 A303715 * A347682 A334383 A019843 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 January 25 23:56 EST 2022. Contains 350572 sequences. (Running on oeis4.)