

A123466


Write the positive integer n in binary. Subdivide the binary n into runs each consisting entirely of 0s or of 1's, where the runs alternate between those of 1s and those of 0s. The sequence gives those numbers n such that there is at least one run of 1s of the same length as at least one run of 0s.


2



2, 5, 10, 11, 12, 13, 18, 19, 20, 21, 22, 23, 25, 26, 29, 34, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 56, 58, 61, 66, 69, 70, 71, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 98, 100, 101, 102, 103, 104
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OFFSET

1,1


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


FORMULA

a(n) ~ n.  Charles R Greathouse IV, Mar 29 2013


EXAMPLE

25 written in binary is 11001. The runs are (11)(00)(1). Since at least one run of 1's (the leftmost run here) is the same length as at least one run of 0s (the only run of 0s here), 25 is included in this sequence.


PROG

(PARI) is(n)=my(ones=List(), zeros=List()); if(n%2, listput(ones, valuation(n+1, 2)); n>>=ones[1]); while(n, listput(zeros, valuation(n, 2)); n>>=zeros[#zeros]; listput(ones, valuation(n+1, 2)); n>>=ones[#ones]); #setintersect(vecsort(Vec(ones), , 8), vecsort(Vec(zeros), , 8))>0 \\ Charles R Greathouse IV, Mar 29 2013


CROSSREFS

Cf. A033015.
Sequence in context: A078310 A138848 A194350 * A144793 A140707 A257086
Adjacent sequences: A123463 A123464 A123465 * A123467 A123468 A123469


KEYWORD

base,easy,nonn


AUTHOR

Leroy Quet, Jul 11 2008


EXTENSIONS

a(16) to a(27) from Ray G. Opao, Jan 08 2009
a(28)a(64) from Lars Blomberg, Dec 09 2011


STATUS

approved



