Problem 1040

[Richard Guy]

1, 1, 1, 1, 1  and any consecutive pair from

1, 6, 41, 281, 1926, 13201, 90481, 620166, 4250681, ...

This is A049685 in OEIS, though this doesn't
mention the problem.

This works for any value of  7.  E.g. with  31
we get

1, 30, 929, 28769, 890910, 27589441, 854381761, ...
but this is not (yet) in OEIS.     R.

On Mon, 10 Oct 2005, stan wagon wrote:

> Problem 1040: A special sum of squares.
>
> Find 7 (not necessarily distinct) positive integers, at least 
> one of which is greater than 1040, such that the sum of their 
> squares is 7 times the product (of the 7 integers).
>
> Extra Credit: I heard this problem from Gerald Heuer (Concordia 
> College), who asked it with 31 instead of 7 in all places. If 
> you can solve this with 31 (or 7), let me know.
>
> Problem 1039.  The region in question consists of two connected 
> areas (shown below), and the sum of the two areas is 2.11503. 
> One interesting way to get this answer in a proved fashion is by 
> the use of interval arithmetic. A more traditional technique, 
> using numerical integration of the upper limit minus the lower 
> in each case, works fine too.
>