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%I #16 Apr 22 2020 19:23:26
%S 0,3,10,15,36,43,54,63,136,147,170,175,204,219,238,255,528,547,586,
%T 591,660,683,694,703,792,819,858,879,924,955,990,1023,2080,2115,2186,
%U 2191,2340,2347,2358,2367,2600,2643,2730,2735,2764,2779,2798,2815,3120,3171
%N a(n) is the least value whose binary representation can be obtained by interleaving (or shuffling) two copies of the binary representation of n.
%C The binary representation of all positive terms are square binary words (see A191755).
%H Rémy Sigrist, <a href="/A330940/b330940.txt">Table of n, a(n) for n = 0..8192</a>
%H Rémy Sigrist, <a href="/A330940/a330940.png">Logarithmic scatterplot of the first difference of the first 2^13 terms</a>
%H Rémy Sigrist, <a href="/A330940/a330940.gp.txt">PARI program for A330940</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F a(2^k) = 2^k*(1+2^(k+1)) = A007582(k+1) for any k >= 0.
%F a(2^k-1) = 4^k-1 = A024036(k) for any k >= 0.
%F a(n) <= A330941(n).
%e The first terms, alongside the binary representation of n and of a(n), are:
%e n a(n) bin(n) bin(a(n))
%e -- ---- ------ ---------
%e 0 0 0 0
%e 1 3 1 11
%e 2 10 10 1010
%e 3 15 11 1111
%e 4 36 100 100100
%e 5 43 101 101011
%e 6 54 110 110110
%e 7 63 111 111111
%e 8 136 1000 10001000
%e 9 147 1001 10010011
%e 10 170 1010 10101010
%e 11 175 1011 10101111
%o (PARI) See Links section.
%Y See A330941 for the maximum variant.
%Y Cf. A007582, A024036, A191755, A193020.
%K nonn,base
%O 0,2
%A _Rémy Sigrist_, Jan 04 2020
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