A062843 Maximum number of ones in the representation of n in any base.

1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 3, 4, 2, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 2, 2, 3, 2, 3, 3, 4, 4, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4

Offset: 1

Author

Erich Friedman, Jul 21 2001

Keywords

• base
• easy
• nonn

Examples

			a(11)=3 since 11 in base 2 is 1011, containing 3 ones.
		

Programs

Maple

seq(max(numboccur(convert(i,base,2),1), numboccur(convert(i,base,3),1), numboccur(convert(i,base,4),2), numboccur(convert(i,base,5),1), numboccur(convert(i,base,6),1), numboccur(convert(i,base,7),1), numboccur(convert(i,base,8),1), numboccur(convert(i,base,9),1), numboccur(convert(i,base,10),1), numboccur(convert(i,base,11),1), numboccur(convert(i,base,12),1), numboccur(convert(i,base,13),1), numboccur(convert(i,base,14),1), numboccur(convert(i,base,15),1), numboccur(convert(i,base,16),1), numboccur(convert(i,base,17),1)),i=1..200);

PARI

ones(n,b)=my(s); while(n,if(n%b==1,s++);n\=b); s
a(n)=if(n<3,return(1)); my(m=hammingweight(n),b=2); while(b++^(m-1)Charles R Greathouse IV, Mar 17 2013

Extensions

Maple code and more terms from Barbara Haas Margolius (b.margolius(AT)csuohio.edu), Oct 10 2001