

A001196


Doublebitters: only even length runs in binary expansion.


20



0, 3, 12, 15, 48, 51, 60, 63, 192, 195, 204, 207, 240, 243, 252, 255, 768, 771, 780, 783, 816, 819, 828, 831, 960, 963, 972, 975, 1008, 1011, 1020, 1023, 3072, 3075, 3084, 3087, 3120, 3123, 3132, 3135, 3264, 3267, 3276, 3279, 3312
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OFFSET

0,2


COMMENTS

Numbers whose set of base 4 digits is {0,3}  Ray Chandler, Aug 03 2004
n such that there exists a permutation p_1, ..., p_n of 1, ..., n such that i + p_i is a power of 4 for every i  Ray Chandler, Aug 03 2004
The first 2^n terms of the sequence could be obtained using the Cantorlike process for the segment [0,4^n1]. E.g., for n=1 we have [0,{1,2},3] such that numbers outside of braces are the first 2 terms of the sequence; for n=2 we have [0,{1,2},3,{4,5,6,7,8,9,10,11},12,{13,14},15] such that the numbers outside of braces are the first 4 terms of the sequence, etc.  Vladimir Shevelev, Dec 17 2012


LINKS

Sean A. Irvine, Table of n, a(n) for n = 0..10000
R. Stephan, Some divideandconquer sequences ...
R. Stephan, Table of generating functions
Index entries for sequences related to binary expansion of n


FORMULA

a(2n) = 4a(n), a(2n+1) = 4a(n) + 3.
a(n) = 3 * A000695(n).


MATHEMATICA

fQ[n_] := Union@ Mod[Length@# & /@ Split@ IntegerDigits[n, 2], 2] == {0}; Select[ Range@ 10000, fQ] (* Or *)
fQ[n_] := Union@ Join[IntegerDigits[n, 4], {0, 3}] == {0, 3}; Select[ Range@ 10000, fQ] (* Robert G. Wilson v, Dec 24 2012 *)


PROG

(Haskell)
a001196 n = if n == 0 then 0 else 4 * a001196 n' + 3 * b
where (n', b) = divMod n 2
 Reinhard Zumkeller, Feb 21 2014


CROSSREFS

3 times the Moserde Bruijn sequence A000695.
Cf. A005823, A097252A097262.
Sequence in context: A022380 A290593 A005392 * A096854 A013191 A009783
Adjacent sequences: A001193 A001194 A001195 * A001197 A001198 A001199


KEYWORD

nonn,base,easy


AUTHOR

N. J. A. Sloane, based on an email from Bart la Bastide (bart(AT)xs4all.nl)


STATUS

approved



