A131813 - OEIS

%I #16 Jan 27 2014 16:24:56

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

%T 11,11,12,12,13,13,14,14,15,9,11,13,15,10,12,14,16,12,15,11,14,17,12,

%U 16,13,16,14,18,12,17,13,17,14,19,14,20,15,12,18,13,18,14,21,13,19,15,13

%N a(n+1) = number of preceding terms that are contained in a(n) in binary; a(0)=0.

%C a(n+1) = #{k: a(k) substring of a(n) in binary representation, 0<=k<=n}.

%C a(A131814(n)) = n and a(m) <> n for m < A131814(n).

%C This is an interesting sequence to listen to. - _N. J. A. Sloane_, Sep 28 2007

%H R. Zumkeller, <a href="/A131813/b131813.txt">Table of n, a(n) for n = 0..25000</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%e a(8) = #{a(0), a(1), a(2), a(3), a(7)} = 5;

%e a(9) = #{a(0), a(1), a(2), a(3), a(5), a(6), a(8)} = 7;

%e a(10) = #{a(1), a(2), a(9)} = 3.

%o (Haskell)

%o import Data.List (isInfixOf)

%o a131813 n = a131813_list !! n

%o a131813_list = 0 : f [[0]] where

%o    f xss = y : f (bin y : xss) where

%o      y = sum $ map (fromEnum . (flip isInfixOf $ head xss)) xss

%o    bin n = if n == 0 then [] else b : bin n' where (n',b) = divMod n 2

%o -- _Reinhard Zumkeller_, May 23 2013

%Y Cf. A007088, A137655, A030308.

%K nonn,base,hear,look

%O 0,4

%A _Reinhard Zumkeller_, Jul 18 2007, Feb 01 2008