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

1,1

Comments

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

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

Links

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

Example

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

Mathematica

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

Prog

(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)<n, if(ones(n, b)>m, return(1))); 0 \\ Charles R Greathouse IV, Mar 19 2013

Crossrefs

Sequence in context: A283052 A088259 A123857 * A101434 A293780 A048168

Adjacent sequences: A217310 A217311 A217312 * A217314 A217315 A217316

Keyword

nonn,base

Author

Benedikt Otten, Mar 17 2013

Status

approved