A058841 - OEIS

%I #13 Dec 21 2018 10:30:21

%S 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 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 3,1,14,9,3,6,7,3,2,2,3,4,3,2,6,4,2

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

%D A. Renyi (1957), Representation for real numbers and their ergodic properties, Acta. Math. Acad. Sci. Hung., 8, 477-493.

%H Reinhard Zumkeller, <a href="/A058841/b058841.txt">Table of n, a(n) for n = 0..1000</a>

%t nmax = 500; r = 3/2; x = 1; (* b = A058840 *) b[0] = b[1] = 1;

%t For[n=2, n <= nmax, n++, x = If[r x > 1, r x - 1, r x]; b[n] = Floor[r x]];

%t 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 (Haskell)

%o import Data.List (group)

%o a058841 n = a058841_list !! n

%o a058841_list =

%o    0 : (map length $ filter ((== 0) . head) $ group a058840_list)

%o -- _Reinhard Zumkeller_, Jul 01 2011

%Y Cf. A058840, A058842.

%K nonn,nice,easy

%O 0,3

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

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

%E Data corrected for n>33 by _Reinhard Zumkeller_, Jul 01 2011