A037863 a(n) = (number of digits <=1) - (number of digits >1) in base 4 representation of n.

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

Offset: 1

Author

Clark Kimberling

Keywords

• base
• sign

Crossrefs

Cf. A110591, A139352.

Programs

Maple

A037863 := proc(n)
    a := 0 ;
    dgs := convert(n,base,4);
    for i from 1 to nops(dgs) do
        if op(i,dgs)<=1 then
            a := a+1 ;
        else
            a := a-1 ;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, Oct 16 2015

PARI

a(n) = my(d=digits(n, 4)); #select(x->(x<=1), d) - #select(x->(x>1), d); \\ Michel Marcus, Jan 27 2025

Formula

a(n) = A110591(n)-2*A139352(n). - R. J. Mathar, Jan 27 2025