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 A293427 #11 Oct 13 2017 06:03:58
%S A293427 1,2,3,5,6,7,10,11,13,14,15,21,22,23,26,29,30,31,42,43,46,47,53,55,58,
%T A293427 59,61,62,85,86,87,91,93,94,95,106,107,109,110,111,118,119,122,123,
%U A293427 127,170,173,174,181,182,183,186,187,190,191,213,214,215,218,219,221,222,223,235,237,238,239,246,247,251,253,254,255,341
%N A293427 Squarefree numbers such that there are no adjacent 0's in their binary expansions.
%H A293427 Antti Karttunen, <a href="/A293427/b293427.txt">Table of n, a(n) for n = 1..10000</a>
%H A293427 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%e A293427 55 is present as 55 = 5*11 is squarefree (in A005117) and A007088(55) = 110111 does not contain two adjacent 0's. However, it is not present in A293430 because floor(55/2) = 27 is not a squarefree number.
%t A293427 Select[Range@ 360, And[SquareFreeQ@ #, SequenceCount[IntegerDigits[#, 2], {0, 0}] == 0] &] (* _Michael De Vlieger_, Oct 11 2017 *)
%o A293427 (PARI)
%o A293427 isA003754(n) = { n=bitor(n, n>>1)+1; n>>=valuation(n, 2); (n==1); }; \\ After _Charles R Greathouse IV_'s Feb 06 2017 code.
%o A293427 n=1; k=1; while(k <= 10000, if(isA003754(n)&&issquarefree(n),write("b293427.txt", k, " ", n);k=k+1); n=n+1;); \\ _Antti Karttunen_, Oct 11 2017
%Y A293427 Intersection of A003754 and A005117.
%Y A293427 A293430 is a subsequence from which this differs for the first time at n=24, where a(24) = 55, a term not present in A293430.
%K A293427 nonn,base
%O A293427 1,2
%A A293427 _Antti Karttunen_, Oct 11 2017