%I
%S 3,7,10,15,21,31,36,42,45,54,63,73,85,91,109,127,136,146,153,170,173,
%T 181,182,187,204,219,221,238,255,273,292,307,341,365,375,409,438,443,
%U 477,511,528,546,561,585,594,614,627,660,682,685,693,725,726,731,750
%N Numbers whose binary expansion is quasiperiodic.
%C The binary representation of a term (ignoring leading zeros) can be covered by (possibly overlapping) occurrences of one of its proper prefix.
%C This sequence contains A121016.
%C For any k > 0, there are A320434(k)/2 terms with binary length k.
%H Rémy Sigrist, <a href="/A320441/a320441.png">Scatterplot of the first difference of the first 100000 terms</a>
%F A020330(a(n)) belongs to the sequence for any n > 0.
%F A297405(a(n)) belongs to the sequence for any n > 0.
%e The first terms, alongside their binary representations and prefixes, are:
%e n a(n) bin(a(n)) prefix
%e    
%e 1 3 11 1
%e 2 7 111 1
%e 3 10 1010 10
%e 4 15 1111 1
%e 5 21 10101 101
%e 6 31 11111 1
%e 7 36 100100 100
%e 8 42 101010 10
%e 9 45 101101 101
%e 10 54 110110 110
%e 11 63 111111 1
%e 12 73 1001001 1001
%o (PARI) isok(w) = { my (tt=0); for (l=1, oo, my (t=w%(2^l)); if (t!=tt, if (t==w, return (0)); my (r=w, g=l); while (g>=0 && r>=t, r \= 2; if (r%
%o (2^l)==t, if (r==t, return (1), g=l))); tt = t)) }
%Y Cf. A020330, A121016, A297405, A320434.
%K nonn,base
%O 1,1
%A _Rémy Sigrist_, Jan 09 2019
