MathDB

5

Part of 1973 Dutch Mathematical Olympiad

Problems(1)

a_{n+1} = a_n - n if a_n >= n , or a_{n+1} = a_n + n if a_n < n

Source: Netherlands - Dutch NMO 1973 p5

1/27/2023
An infinite sequence of integers a1,a2,a3,...a_1,a_2,a_3, ... is given with a1=0a_1 = 0 and further holds for every natural number nn that an+1=an−na_{n+1} = a_n - n if an≥na_n \ge n and an+1=an+na_{n+1} = a_n + n if an<na_n < n . (a) Prove that there are infinitely many numbers in the sequence equal to 00. (b) Express in terms of kk the ordinal number of the kek^e number from the sequence, which is equal to 00.
recurrence relationSequencealgebra