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

0, 110, 1110, 0, 10, 1110, 11110, 0, 0, 10, 0, 110, 10, 10, 11110, 0, 110, 11110, 111110, 0, 0, 0, 10, 0, 0, 110, 0, 10, 10, 0, 1110, 10, 0, 10, 10, 110, 110, 10, 111110, 0, 0, 110, 0, 1110, 10, 110, 111110, 0, 1110, 111110, 1111110, 0, 0, 0, 0, 10, 0, 0

Offset

1,2

Comments

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.

Links

Rick L. Shepherd, Table of n, a(n) for n = 1..100000

Example

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).

Prog

(PARI)
/* Calculate terms_wanted terms starting with n: Binary values*/
/* of n, n + 1, n + 2, ..., are concatenated and each term is */
/* the string of all bits up to and including the next zero.  */
/* (Note: Behavior of PARI binary function is such that if    */
/* n < 0 is used, binary values of |n|, |n+1|, |n+2|, ...,    */
/* are concatenated here.)                                    */
/*                                                            */
{a(n, terms_wanted) =
local(v = vector(terms_wanted), term = 0, s = "", b, m, p);
while(term<terms_wanted,
  b = binary(n);
  m = matsize(b)[2];
  p = 1;
  while(p<=m && term<terms_wanted,
    s = concat(s, Str(b[p]));
    if(b[p]==0,
      term++;
      v[term] = eval(s);
      s = "";
    );
    p++;
  );
  n++;
); return(v)}
A213087 = a(0, 100000);
for(n=1, 100000, write("b213087.txt", n, " ", A213087[n]))
(Haskell)
a213087 n = a213087_list !! (n-1)
a213087_list = f a030190_list where
   f xs = foldl1 (\v d -> 10 * v + d) (ys ++ [0]) : f zs where
          (ys, _:zs) = span (/= 0) xs
-- Reinhard Zumkeller, Jun 30 2012

Crossrefs

Cf. A209355, A105279, A007088.

Cf. A030190.

Sequence in context: A159484 A283219 A283137 * A284244 A232781 A248468

Adjacent sequences: A213084 A213085 A213086 * A213088 A213089 A213090

Keyword

nonn,base,easy

Author

Rick L. Shepherd, Jun 07 2012

Status

approved