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.

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

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: A368183 A367905 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