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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

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: A068432 A134668 A039963 * A154269 A036987 A181101

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

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Last modified October 16 12:59 EDT 2018. Contains 316263 sequences. (Running on oeis4.)