%I
%S 6724,6725,6726,6727,7844,7845,7846,7847,8964,8965,8966,8967,12832,
%T 12833,12834,12835,12836,12837,12838,12839,12840,12841,12842,12843,
%U 12844,12845,12846,12847,12848,12849,12850,12851,12852,12853,12854,12855,12856,12857,12858
%N Numbers n such that their decimal expansion can be split into at least two parts whose binary equivalents can be concatenated (in the same order) to form the binary expansion of the original number n.
%C There are exactly 96 terms in this sequence smaller than 10^9.
%C There are possibly an infinite number of these numbers.
%D Andreas Boe, The Wasp Nest, Amazon Books, 2013
%H Andreas Boe and Giovanni Resta, <a href="/A237041/b237041.txt">Table of n, a(n) for n = 1..2838</a> (terms < 1.3*10^11, 92 terms from Andreas Boe)
%H Andreas Boe, <a href="http://nerdology.info/nerdologyinfo/thewaspnest/spoilers/numbers/12834/boenumbers.html">Boe Numbers</a>
%H Giovanni Resta, <a href="/A237041/a237041.txt">Decompositions for terms < 1.3*10^11</a>
%e 6724 > 6.72.4 > 110.1001000.100 > 1101001000100 > 6724.
%t okQ[t_,d_,b_] := Catch[Block[{pw = 10, bL, y, r}, d == b && d < t && Throw@True; d < 10 && Throw@False; While[d > pw, y = Mod[d, pw]; bL = 2^If[y == 0, 1, IntegerLength[y, 2]]; Mod[b, bL] == y && okQ[t, Floor[d/pw], Floor[b/bL]] && Throw@True; pw *= 10]; False]]; okQ[n_] := okQ[n, n, n]; Select[Range[9, 15000], okQ] (* _Giovanni Resta_, Feb 03 2014 *)
%K nonn,base
%O 1,1
%A _Andreas Boe_, Feb 02 2014
