A243109 -id:A243109

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A037870

a(n) = (1/2)*Sum{|d(i)-e(i)|}, where Sum{d(i)*2^i} is base 2 representation of n and e(i) are digits d(i) in nonincreasing order, for i=0,1,...,m.

+10
3

0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2

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OFFSET

1,12

COMMENTS

a(n) is also the minimum number of bit swap operations that needs to be performed to pack all the bits of n to the right. - Philippe Beaudoin, Aug 20 2014

a(n) = 0 if A243109(n) = n; 1 + a(A243109(n)) otherwise. - Philippe Beaudoin, Aug 20 2014

The index of the k-th record of this sequence is A020522(k) and corresponds to k ones followed by k zeros. - Philippe Beaudoin, Aug 20 2014

LINKS

Philippe Beaudoin, Table of n, a(n) for n = 1..10000

MAPLE

a:= proc(n) local L, m;

L:= convert(n, base, 2);

m:= convert(L, `+`);

m - convert(L[1..m], `+`);

end proc:

seq(a(n), n=1..100); # Robert Israel, Aug 20 2014

PROG

(PARI) a(n) = {d = binary(n); e = vecsort(d); sum(i=1, #d, abs(d[i]-e[i]))/2; } \\ Michel Marcus, Aug 20 2014

KEYWORD

nonn,base

AUTHOR

Clark Kimberling

EXTENSIONS

Definition swapped with A037879. - R. J. Mathar, Oct 19 2015

STATUS

approved

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