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A062843
Maximum number of ones in the representation of n in any base.
1
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
1,3
EXAMPLE
a(11)=3 since 11 in base 2 is 1011, containing 3 ones.
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);
PROG
(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)<n, m=max(m, ones(n, b))); m \\ Charles R Greathouse IV, Mar 17 2013
CROSSREFS
Sequence in context: A087133 A324292 A196941 * A136164 A182860 A328830
KEYWORD
base,easy,nonn
AUTHOR
Erich Friedman, Jul 21 2001
EXTENSIONS
Maple code and more terms from Barbara Haas Margolius (b.margolius(AT)csuohio.edu), Oct 10 2001
STATUS
approved