A037882 a(n)=(1/2)*Sum{|d(i)-e(i)|} where Sum{d(i)*5^i} is the base 5 representation of n and e(i) are the digits d(i) in nondecreasing order.

0, 0, 0, 0, 0, 0, 1, 2, 3, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 0, 0, 1, 2, 3, 1, 1, 1, 2, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 0, 1, 2, 3, 4, 0, 0, 1, 2, 3, 0, 0, 0, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 1, 2, 3, 4, 0, 0, 1, 2, 3, 0, 0, 0, 1, 2, 0

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

Starts to differ from A037846 at n=137 = 1022_5. -R. J. Mathar, Aug 05 2025

Programs

Maple

A037882 := proc(n)
    local a,dgs,dgsE ;
    a := 0 ;
    dgs := convert(n,base,5);
    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

Extensions

Definition swapped with A037873. - R. J. Mathar, Oct 19 2015