A217313 Numbers for which there exist a base in which n contains more 1's than in binary.

4, 8, 16, 32, 40, 64, 112, 128, 129, 130, 148, 256, 257, 258, 259, 260, 274, 280, 292, 328, 336, 337, 352, 364, 388, 392, 400, 448, 512, 580, 608, 656, 768, 769, 770, 772, 776, 784, 832, 850, 1024, 1025, 1026, 1030, 1032, 1036, 1040, 1042, 1048, 1056, 1057, 1058, 1060, 1064, 1065

Offset: 1

Author

Benedikt Otten, Mar 17 2013

Keywords

• nonn
• base

Comments

Numbers n for which A062843(n) != A000120(n).

Every number of the form 2^m with m > 1 is included in the list.

Examples

			40 is 111 (3 ones) in base 3 and 101000 (2 ones) in base 2, therefore it is in the sequence.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Programs

Mathematica

Select[Table[n, {n, 1, 1000}], Max[Table[Count[IntegerDigits[#, b], 1], {b, 2, # + 1}]] != Count[IntegerDigits[#, 2], 1] &]

PARI

ones(n, b)=my(s); while(n, if(n%b==1, s++); n\=b); s
is(n)=if(n<4, return(0)); my(m=hammingweight(n), b=2); while(b++^(m-1)m,return(1))); 0 \\ Charles R Greathouse IV, Mar 19 2013