%I
%S 14,24,40,44,62,64,70,75,81,84,98,99,114,117,122,127,133,134,140,159,
%T 167,175,184,188,189,190,200,212,215,232,234,273,274,282,292,300,318,
%U 348,377,440,516,527,620
%N Numbers k such that 2^k contains 2^4=16 as its largest proper substring of the form 2^m (probably finite).
%e 2^14 = {16}384;
%e 2^24 = {16}7772{16};
%e 2^40 = 109951{16}27776.
%t sub2[n_] := Block[{s = ToString[2^n], k = n  1}, While[k >= 0 && ! StringContainsQ[s, ToString[2^k]], k]; k]; Select[Range[2000], sub2[#] == 4 &] (* _Giovanni Resta_, Oct 14 2019 *)
%Y Cf. A033921.
%K nonn,base
%O 1,1
%A _Patrick De Geest_, Jun 15 1998
