This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A217313 #22 May 13 2013 01:54:22
%S A217313 4,8,16,32,40,64,112,128,129,130,148,256,257,258,259,260,274,280,292,
%T A217313 328,336,337,352,364,388,392,400,448,512,580,608,656,768,769,770,772,
%U A217313 776,784,832,850,1024,1025,1026,1030,1032,1036,1040,1042,1048,1056,1057,1058,1060,1064,1065
%N A217313 Numbers for which there exist a base in which n contains more 1's than in binary.
%C A217313 Numbers n for which A062843(n) != A000120(n).
%C A217313 Every number of the form 2^m with m > 1 is included in the list.
%H A217313 Charles R Greathouse IV, <a href="/A217313/b217313.txt">Table of n, a(n) for n = 1..10000</a>
%e A217313 40 is 111 (3 ones) in base 3 and 101000 (2 ones) in base 2, therefore it is in the sequence.
%t A217313 Select[Table[n, {n, 1, 1000}], Max[Table[Count[IntegerDigits[#, b], 1], {b, 2, # + 1}]] != Count[IntegerDigits[#, 2], 1] &]
%o A217313 (PARI) ones(n, b)=my(s); while(n, if(n%b==1, s++); n\=b); s
%o A217313 is(n)=if(n<4, return(0)); my(m=hammingweight(n), b=2); while(b++^(m-1)<n, if(ones(n, b)>m,return(1))); 0 \\ _Charles R Greathouse IV_, Mar 19 2013
%K A217313 nonn,base
%O A217313 1,1
%A A217313 _Benedikt Otten_, Mar 17 2013