This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A058840 From Renyi's "beta expansion of 1 in base 3/2": sequence gives y(0), y(1), ... 3
 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Let r be a real number strictly between 1 and 2, x any real number between 0 and 1; define y = (y(i)) by x(0) = x; x(i+1) = r*x(i)-1 if r*x(i)>1 and r*x(i) otherwise; y(i) = integer part of x(i+1): y = (y(i)) is an infinite word on the alphabet (0,1). Here we take r = 3/2 and x = 1. REFERENCES A. Renyi (1957), Representation for real numbers and their ergodic properties, Acta. Math. Acad. Sci. Hung., 8, 477-493. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 MATHEMATICA r = 3/2; x = 1; a[0] = a[1] = 1; For[n = 2, n<105, n++, x = If[r x > 1, r x - 1, r x]; a[n] = Floor[r x]]; Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Dec 21 2018, a solution I owe to Benoit Cloitre *) PROG (Haskell) import data.ratio ((%), numerator, denominator) a058840 n = a058840_list !! n a058840_list = 1 : renyi' 1 where    renyi' x = y : renyi' r  where       (r, y) | q > 1     = (q - 1, 1)              | otherwise = (q, 0)       q = 3%2 * x -- Reinhard Zumkeller, Jul 01 2011 CROSSREFS Cf. A058841, A058842. Sequence in context: A039963 A267537 A183919 * A266155 A262683 A321083 Adjacent sequences:  A058837 A058838 A058839 * A058841 A058842 A058843 KEYWORD nonn,nice,easy AUTHOR Claude Lenormand (claude.lenormand(AT)free.fr), Jan 05 2001 EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Feb 22 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 23 04:40 EST 2019. Contains 319370 sequences. (Running on oeis4.)