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A330941 a(n) is the greatest value whose binary representation can be obtained by interleaving (or shuffling) two copies of the binary representation of n.

%I A330941 #18 Apr 22 2020 19:23:34
%S A330941 0,3,12,15,48,53,60,63,192,201,212,219,240,245,252,255,768,785,804,
%T A330941 819,848,853,876,887,960,969,980,987,1008,1013,1020,1023,3072,3105,
%U A330941 3140,3171,3216,3237,3276,3303,3392,3401,3412,3435,3504,3509,3548,3567,3840,3857
%N A330941 a(n) is the greatest value whose binary representation can be obtained by interleaving (or shuffling) two copies of the binary representation of n.
%C A330941 The binary representation of all positive terms are square binary words (see A191755).
%H A330941 Rémy Sigrist, <a href="/A330941/b330941.txt">Table of n, a(n) for n = 0..8192</a>
%H A330941 Rémy Sigrist, <a href="/A330941/a330941.png">Logarithmic scatterplot of the first difference of the first 2^13 terms</a>
%H A330941 Rémy Sigrist, <a href="/A330941/a330941.gp.txt">PARI program for A330941</a>
%H A330941 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A330941 a(2^k) = 3*4^k = A002001(k+1) for any k >= 0.
%F A330941 a(2^k-1) = 4^k-1 = A024036(k) for any k >= 0.
%F A330941 a(n) >= A330940(n).
%e A330941 The first terms, alongside the binary representations of n and of a(n), are:
%e A330941   n   a(n)  bin(n)  bin(a(n))
%e A330941   --  ----  ------  ----------
%e A330941    0     0       0           0
%e A330941    1     3       1          11
%e A330941    2    12      10        1100
%e A330941    3    15      11        1111
%e A330941    4    48     100      110000
%e A330941    5    53     101      110101
%e A330941    6    60     110      111100
%e A330941    7    63     111      111111
%e A330941    8   192    1000    11000000
%e A330941    9   201    1001    11001001
%e A330941   10   212    1010    11010100
%e A330941   11   219    1011    11011011
%e A330941   12   240    1100    11110000
%o A330941 (PARI) See Links section.
%Y A330941 See A330940 for the minimum variant.
%Y A330941 Cf. A002001, A024036, A191755, A193020.
%K A330941 nonn,base
%O A330941 0,2
%A A330941 _Rémy Sigrist_, Jan 04 2020