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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. 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 (list; graph; refs; listen; history; text; internal format)
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

CROSSREFS

Sequence in context: A033665 A104234 A321926 * A250205 A326017 A290307

Adjacent sequences:  A037867 A037868 A037869 * A037871 A037872 A037873

KEYWORD

nonn,base

AUTHOR

Clark Kimberling

EXTENSIONS

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

STATUS

approved

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Last modified September 21 19:59 EDT 2019. Contains 327282 sequences. (Running on oeis4.)