This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A330940 #16 Apr 22 2020 19:23:26 %S A330940 0,3,10,15,36,43,54,63,136,147,170,175,204,219,238,255,528,547,586, %T A330940 591,660,683,694,703,792,819,858,879,924,955,990,1023,2080,2115,2186, %U A330940 2191,2340,2347,2358,2367,2600,2643,2730,2735,2764,2779,2798,2815,3120,3171 %N A330940 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 A330940 The binary representation of all positive terms are square binary words (see A191755). %H A330940 Rémy Sigrist, <a href="/A330940/b330940.txt">Table of n, a(n) for n = 0..8192</a> %H A330940 Rémy Sigrist, <a href="/A330940/a330940.png">Logarithmic scatterplot of the first difference of the first 2^13 terms</a> %H A330940 Rémy Sigrist, <a href="/A330940/a330940.gp.txt">PARI program for A330940</a> %H A330940 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a> %F A330940 a(2^k) = 2^k*(1+2^(k+1)) = A007582(k+1) for any k >= 0. %F A330940 a(2^k-1) = 4^k-1 = A024036(k) for any k >= 0. %F A330940 a(n) <= A330941(n). %e A330940 The first terms, alongside the binary representation of n and of a(n), are: %e A330940 n a(n) bin(n) bin(a(n)) %e A330940 -- ---- ------ --------- %e A330940 0 0 0 0 %e A330940 1 3 1 11 %e A330940 2 10 10 1010 %e A330940 3 15 11 1111 %e A330940 4 36 100 100100 %e A330940 5 43 101 101011 %e A330940 6 54 110 110110 %e A330940 7 63 111 111111 %e A330940 8 136 1000 10001000 %e A330940 9 147 1001 10010011 %e A330940 10 170 1010 10101010 %e A330940 11 175 1011 10101111 %o A330940 (PARI) See Links section. %Y A330940 See A330941 for the maximum variant. %Y A330940 Cf. A007582, A024036, A191755, A193020. %K A330940 nonn,base %O A330940 0,2 %A A330940 _Rémy Sigrist_, Jan 04 2020