A037879 a(n) = (1/2)*Sum{|d(i)-e(i)|} where Sum{d(i)*2^i} is the base-2 representation of n and {e(i)} are digits {d(i)} in nondecreasing order.

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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

A037879 := proc(n)
        local a,dgs,dgsE ;
        a := 0 ;
        dgs := convert(n,base,2);
        dgsE := sort(dgs) ;
        for i from 1 to nops(dgs) do
                a := a+ abs(op(i,dgs)-op(i,dgsE)) ;
        end do:
        a/2 ;
end proc: # R. J. Mathar, Oct 19 2015

Formula

a(2*n) = a(n). a(2*n+1) is either a(n) or a(n) + 1. - Robert Israel, Feb 08 2019

Extensions

Definition swapped with A037870. - R. J. Mathar, Oct 19 2015