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A062843
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Maximum number of ones in the representation of n in any base.
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1
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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
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OFFSET
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1,3
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LINKS
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EXAMPLE
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a(11)=3 since 11 in base 2 is 1011, containing 3 ones.
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MAPLE
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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);
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PROG
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(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
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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Maple code and more terms from Barbara Haas Margolius (b.margolius(AT)csuohio.edu), Oct 10 2001
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STATUS
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approved
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