cp's OEIS Frontend

A213087 Concatenate the binary representations of the nonnegative integers and form successive terms by inserting a comma after each zero.

%I A213087 #9 Jun 30 2012 08:14:57
%S A213087 0,110,1110,0,10,1110,11110,0,0,10,0,110,10,10,11110,0,110,11110,
%T A213087 111110,0,0,0,10,0,0,110,0,10,10,0,1110,10,0,10,10,110,110,10,111110,
%U A213087 0,0,110,0,1110,10,110,111110,0,1110,111110,1111110,0,0,0,0,10,0,0
%N A213087 Concatenate the binary representations of the nonnegative integers and form successive terms by inserting a comma after each zero.
%C A213087 This sequence has the same property as A209355, namely, each term in this sequence occurs infinitely often in runs of every finite length >= 1. This sequence, however, contains an infinite number of distinct terms, the same digit strings as occur uniquely and sorted in A105279.
%H A213087 Rick L. Shepherd, <a href="/A213087/b213087.txt">Table of n, a(n) for n = 1..100000</a>
%e A213087 The binary representations of 0, 1, 2, 3, 4 are 0, 1, 10, 11, 100, so concatenation gives 011011100, which, when commas are inserted after each zero, produces 0, 110, 1110, 0, terms a(1) through a(4).
%o A213087 (PARI)
%o A213087 /* Calculate terms_wanted terms starting with n: Binary values*/
%o A213087 /* of n, n + 1, n + 2, ..., are concatenated and each term is */
%o A213087 /* the string of all bits up to and including the next zero.  */
%o A213087 /* (Note: Behavior of PARI binary function is such that if    */
%o A213087 /* n < 0 is used, binary values of |n|, |n+1|, |n+2|, ...,    */
%o A213087 /* are concatenated here.)                                    */
%o A213087 /*                                                            */
%o A213087 {a(n, terms_wanted) =
%o A213087 local(v = vector(terms_wanted), term = 0, s = "", b, m, p);
%o A213087 while(term<terms_wanted,
%o A213087   b = binary(n);
%o A213087   m = matsize(b)[2];
%o A213087   p = 1;
%o A213087   while(p<=m && term<terms_wanted,
%o A213087     s = concat(s,Str(b[p]));
%o A213087     if(b[p]==0,
%o A213087       term++;
%o A213087       v[term] = eval(s);
%o A213087       s = "";
%o A213087     );
%o A213087     p++;
%o A213087   );
%o A213087   n++;
%o A213087 ); return(v)}
%o A213087 A213087 = a(0, 100000);
%o A213087 for(n=1, 100000, write("b213087.txt", n, " ", A213087[n]))
%o A213087 (Haskell)
%o A213087 a213087 n = a213087_list !! (n-1)
%o A213087 a213087_list = f a030190_list where
%o A213087    f xs = foldl1 (\v d -> 10 * v + d) (ys ++ [0]) : f zs where
%o A213087           (ys, _:zs) = span (/= 0) xs
%o A213087 -- _Reinhard Zumkeller_, Jun 30 2012
%Y A213087 Cf. A209355, A105279, A007088.
%Y A213087 Cf. A030190.
%K A213087 nonn,base,easy
%O A213087 1,2
%A A213087 _Rick L. Shepherd_, Jun 07 2012