A086267 a(n) = 3 + (H(n) mod 6) + floor(r) where H()=A005185() and r = (H(n) - 2*H(n+1) + H(n+2) - 4) / H(n).

1, 0, 2, 5, 4, 5, 7, 7, 2, 2, 2, 4, 4, 4, 6, 5, 6, 7, 7, 2, 2, 3, 2, 6, 4, 4, 6, 6, 7, 6, 4, 7, 7, 4, 5, 3, 4, 6, 5, 6, 7, 7, 2, 2, 2, 3, 2, 5, 3, 3, 2, 7, 4, 2, 3, 6, 5, 2, 4, 4, 5, 4, 7, 6, 3, 4, 8, 5, 5, 7, 3, 4, 6, 5, 7, 5, 2, 6, 7, 3, 4, 3, 3, 6, 4, 5, 7, 7, 6, 2, 2, 2, 2, 3, 2, 7, 7, 6, 2, 5, 2, 2, 3, 4, 3

Offset: 1

Author

Roger L. Bagula, Aug 28 2003

Keywords

• nonn
• obsc

Programs

Maple

A005185 := proc(n)
        option remember;
        if n<=2 then
                1
        elif n > procname(n-1) and n > procname(n-2) then
                procname(n-procname(n-1))+procname(n-procname(n-2));
        end if;
end proc:
A086267 := proc(n)
        local H ;
        H := A005185(n) ;
        H-2*A005185(n+1)+A005185(n+2)-4;
        %/H ;
        3+ floor(%)+ (H mod 6) ;
end proc:
seq(A086267(n),n=1..50) ; # R. J. Mathar, Oct 10 2011

Mathematica

Hofstadter[n_Integer?Positive] := Hofstadter[n] = Hofstadter[n - Hofstadter[n-1]] + Hofstadter[n - Hofstadter[n-2]] Hofstadter[1] = Hofstadter[2] = 1 Digits=502 a=Table[Hofstadter[n], {n, 1, Digits}]; b=Table[Floor[(a[[n]]-2*a[[n+1]]+a[[n+2]]-4)/a[[n]]]+Mod[a[[n]], 6]+3, {n, 1, Digits-2}] ListPlot[b]