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%I #17 Oct 14 2019 03:45:54
%S 103,267,279,287,404,503,511,515,657,685,745,763,883,890,922,946,973,
%T 991,1011,1087,1114,1121,1164,1197,1209,1272,1274,1283,1302,1316,1328,
%U 1360,1378,1432,1445,1478,1509,1511,1542,1565,1571,1584,1627,1672,1678
%N Numbers k such that 2^k contains 2^11=2048 as its largest proper substring of the form 2^m.
%e 2^103 = 10141{2048}01825835211973625643008.
%t sub2[n_] := Block[{s = ToString[2^n], k = n-1}, While[k >= 0 && ! StringContainsQ[ s, ToString[2^k]], k--]; k]; Select[Range[1000], sub2[#] == 11 &] (* _Giovanni Resta_, Oct 14 2019 *)
%Y Cf. A033921.
%K nonn,base
%O 1,1
%A _Patrick De Geest_, Jun 15 1998