Confirmation

[Max A.]

I've got

x = 8334201245
f(x) = 17364786429187398690

I've also checked that the value f(n) was non-decreasing during
computations. Since f(n+1) < f(n)+n+3364 and f(x)+x+3364 < 2^64, that
means no overflow in 64-bit unsigned integer happened.

Max

On 11/21/06, David Wilson <davidwwilson at comcast.net> wrote:
>
>
> Define
>
>     f(1) = 1
>     f(n+1) = f(n) + (f(n) mod n+3364).
>
> I wrote a computer program to find the smallest x with
>
>     x+3365 divides f(x)
>
> The value of x found is just under 8,350,000,000 and the corresponding f(x)
> just under 2^64. Although my program included an overflow check, I am still
> not comfortable because this value of f(x) is close to my 64-bit unsigned
> integer size.
>
> Could someone with a fast computer, preferably a UNIX box, please confirm or
> refute my values?