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%I #9 Jun 30 2012 08:14:57
%S 0,110,1110,0,10,1110,11110,0,0,10,0,110,10,10,11110,0,110,11110,
%T 111110,0,0,0,10,0,0,110,0,10,10,0,1110,10,0,10,10,110,110,10,111110,
%U 0,0,110,0,1110,10,110,111110,0,1110,111110,1111110,0,0,0,0,10,0,0
%N Concatenate the binary representations of the nonnegative integers and form successive terms by inserting a comma after each zero.
%C 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 Rick L. Shepherd, <a href="/A213087/b213087.txt">Table of n, a(n) for n = 1..100000</a>
%e 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 (PARI)
%o /* Calculate terms_wanted terms starting with n: Binary values*/
%o /* of n, n + 1, n + 2, ..., are concatenated and each term is */
%o /* the string of all bits up to and including the next zero. */
%o /* (Note: Behavior of PARI binary function is such that if */
%o /* n < 0 is used, binary values of |n|, |n+1|, |n+2|, ..., */
%o /* are concatenated here.) */
%o /* */
%o {a(n, terms_wanted) =
%o local(v = vector(terms_wanted), term = 0, s = "", b, m, p);
%o while(term<terms_wanted,
%o b = binary(n);
%o m = matsize(b)[2];
%o p = 1;
%o while(p<=m && term<terms_wanted,
%o s = concat(s,Str(b[p]));
%o if(b[p]==0,
%o term++;
%o v[term] = eval(s);
%o s = "";
%o );
%o p++;
%o );
%o n++;
%o ); return(v)}
%o A213087 = a(0, 100000);
%o for(n=1, 100000, write("b213087.txt", n, " ", A213087[n]))
%o (Haskell)
%o a213087 n = a213087_list !! (n-1)
%o a213087_list = f a030190_list where
%o f xs = foldl1 (\v d -> 10 * v + d) (ys ++ [0]) : f zs where
%o (ys, _:zs) = span (/= 0) xs
%o -- _Reinhard Zumkeller_, Jun 30 2012
%Y Cf. A209355, A105279, A007088.
%Y Cf. A030190.
%K nonn,base,easy
%O 1,2
%A _Rick L. Shepherd_, Jun 07 2012
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