A058841 From Renyi's "beta expansion of 1 in base 3/2": sequence gives lengths of runs of 0's in A058840.

0, 1, 5, 2, 2, 1, 9, 6, 4, 6, 2, 2, 1, 11, 3, 2, 7, 2, 5, 4, 6, 3, 3, 5, 2, 4, 7, 7, 2, 5, 3, 4, 2, 3, 5, 5, 2, 2, 2, 2, 4, 3, 10, 5, 5, 2, 1, 6, 1, 5, 2, 3, 2, 3, 3, 2, 9, 6, 9, 6, 8, 2, 7, 5, 3, 2, 2, 4, 3, 1, 14, 9, 3, 6, 7, 3, 2, 2, 3, 4, 3, 2, 6, 4, 2

Offset: 0

Author

Claude Lenormand (claude.lenormand(AT)free.fr), Jan 05 2001

Keywords

• nonn
• nice
• easy

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..1000

Crossrefs

Cf. A058840, A058842.

Programs

Haskell

import Data.List (group)
a058841 n = a058841_list !! n
a058841_list =
   0 : (map length $ filter ((== 0) . head) $ group a058840_list)
-- Reinhard Zumkeller, Jul 01 2011

Mathematica

nmax = 500; r = 3/2; x = 1; (* b = A058840 *) b[0] = b[1] = 1;
For[n=2, n <= nmax, n++, x = If[r x > 1, r x - 1, r x]; b[n] = Floor[r x]];
Join[{0}, Length /@ Select[Split[Table[b[n], {n, 0, nmax}]], #[[1]] == 0&]] (* Jean-François Alcover, Dec 21 2018, using Benoit Cloitre's code for A058840 *)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Feb 22 2001

Data corrected for n>33 by Reinhard Zumkeller, Jul 01 2011