The following are the smallest 9 elements of an infinite set of integers:
What rule generates the set? What are the next two values?
(In reply to Answer
by K Sengupta)
Each term of the given sequence is an automorphic number. We know that an autiomorphic number is a nonnegative integer T (say) having S digits, such that the last s digits of T^2 when read from left to right constitute the original number, that is T.
376^2 = 141376, where 376 is has three digits and the last three digits of 376^2 is indeed 376. Hence, 376 is an automorphic number.
We now observe that the two numbers higher than 9376 with this property are 90625 and 109376, since:
90625^2 = 8212890625, and:
109376^2 = 11963109376.
Consequently, the required next two terms of the given sequence are 90625 and 109376.
Edited on May 19, 2008, 5:08 am