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

%I A058841 #13 Dec 21 2018 10:30:21
%S A058841 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,
%T A058841 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,
%U A058841 3,1,14,9,3,6,7,3,2,2,3,4,3,2,6,4,2
%N A058841 From Renyi's "beta expansion of 1 in base 3/2": sequence gives lengths of runs of 0's in A058840.
%D A058841 A. Renyi (1957), Representation for real numbers and their ergodic properties, Acta. Math. Acad. Sci. Hung., 8, 477-493.
%H A058841 Reinhard Zumkeller, <a href="/A058841/b058841.txt">Table of n, a(n) for n = 0..1000</a>
%t A058841 nmax = 500; r = 3/2; x = 1; (* b = A058840 *) b[0] = b[1] = 1;
%t A058841 For[n=2, n <= nmax, n++, x = If[r x > 1, r x - 1, r x]; b[n] = Floor[r x]];
%t A058841 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 *)
%o A058841 (Haskell)
%o A058841 import Data.List (group)
%o A058841 a058841 n = a058841_list !! n
%o A058841 a058841_list =
%o A058841    0 : (map length $ filter ((== 0) . head) $ group a058840_list)
%o A058841 -- _Reinhard Zumkeller_, Jul 01 2011
%Y A058841 Cf. A058840, A058842.
%K A058841 nonn,nice,easy
%O A058841 0,3
%A A058841 Claude Lenormand (claude.lenormand(AT)free.fr), Jan 05 2001
%E A058841 More terms from Larry Reeves (larryr(AT)acm.org), Feb 22 2001
%E A058841 Data corrected for n>33 by _Reinhard Zumkeller_, Jul 01 2011