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%I #18 Mar 16 2021 20:06:00
%S 224,278,286,473,502,510,645,656,698,744,871,889,909,921,955,960,966,
%T 972,1010,1062,1086,1113,1163,1182,1200,1201,1208,1271,1273,1282,1315,
%U 1327,1377,1431,1444,1510,1541,1550,1564,1570,1583,1610,1626,1674,1677
%N Numbers k such that 2^k contains 2^10 = 1024 as its largest proper substring of the form 2^m.
%t sub2[n_] := Block[{s = ToString[2^n], k = n - 1}, While[k >= 0 && ! StringContainsQ[s, ToString[2^k]], k--]; k]; Select[Range[1677], sub2[#] == 10 &] (* _Giovanni Resta_, Oct 14 2019 *)
%Y Cf. A000079, A033921.
%K nonn,base
%O 1,1
%A _Patrick De Geest_, Jun 15 1998
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