An octagonal number is a number that is represented by the set of figures given below.

A certain octagonal number is the sum of the squares of three terms in an arithmetic sequence with a common difference of 704. What is that octagonal number?

(In reply to For starters by e.g.)

This UBASIC program uses e.g.'s expressions for the square sum and the octagonal numbers:

list
   10   for N=1 to 1000000
   20    V=3*N*N-2*N-2*704*704
   30    if V@3=0 and V>0 then
   40      :M=int(sqrt(V/3)+0.5)
   50      :if M*M=V/3 then
   60        :print M,3*m*m+2*704*704
   70   next
OK

run
 2836    25119920
OK

The result indicates the octagonal number is 25,119,920 and the middle term in the arithmetic sequence is 2,836.

25,119,920 is the 2,894-th octagonal number, based on the formula e.g. found.

Posted by Charlie on 2006-06-13 11:07:39