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

Author

Rick L. Shepherd, Jun 07 2012

Keywords

• nonn
• base
• easy

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.

Examples

			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).
		

Links

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

Crossrefs

Cf. A209355, A105279, A007088.

Cf. A030190.

Programs

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

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(termA213087 = a(0, 100000);
for(n=1, 100000, write("b213087.txt", n, " ", A213087[n]))