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A123466
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Write the positive integer n in binary. Subdivide the binary n into runs each consisting entirely of 0's or of 1's, where the runs alternate between those of 1's and those of 0's. The sequence gives those numbers n such that there is at least one run of 1's of the same length as at least one run of 0's.
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2
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) ~ n. - Charles R Greathouse IV, Mar 29 2013
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EXAMPLE
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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 0's (the only run of 0's here), 25 is included in this sequence.
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PROG
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(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
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CROSSREFS
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Cf. A033015.
Sequence in context: A138848 A194350 A182179 * A144793 A140707 A257086
Adjacent sequences: A123463 A123464 A123465 * A123467 A123468 A123469
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KEYWORD
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base,easy,nonn
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AUTHOR
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Leroy Quet, Jul 11 2008
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EXTENSIONS
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a(16) to a(27) from Ray G. Opao, Jan 08 2009
a(28)-a(64) from Lars Blomberg, Dec 09 2011
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STATUS
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approved
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