Define a function f mapping positive integers to positive integers by f(1)=1, and f(n)=f(n-1)+n if f(n-1)<=n and f(n)=f(n-1)-n if f(n-1)>n

For n≥2,
i) Find the smallest integer n such that f(n) = 1,000,000
ii) Find the smallest integer n such that f(n) = 2,000,000

Answers have a *

Interesting fn!

rabbit-3:~ lord$ fn

     n         f(n)

   671396    1000000*

  1985808    1000000

  7957423    2000000*

rabbit-3:~ lord$ more fn.f

        program fn

        implicit none

        integer f(8000000),i

        f(1)=1

           do i=2,8000000

                if(f(i-1).le.i)then

                f(i)=f(i-1)+i

                else

                f(i)=f(i-1)-i

                endif

       if(f(i).eq.1000000.or.f(i).eq.2000000)print1,i,f(i)

1          format(i9,2x,i9)

           enddo

        end

Edited on August 15, 2019, 7:19 am

Posted by Steven Lord on 2019-08-15 07:18:53