MathDB

5

Part of 2016 Lusophon Mathematical Olympiad

Problems(1)

lusophone sequence: 1, 1 (x prime or +1), .., .. (x prime or +1), 2016

Source: Lusophon 2016 CPLP P5

8/29/2018
A numerical sequence is called lusophone if it satisfies the following three conditions: i) The first term of the sequence is number 11. ii) To obtain the next term of the sequence we can multiply the previous term by a positive prime number (2,3,5,7,11,...2,3,5,7,11, ...) or add 11. (iii) The last term of the sequence is the number 20162016. For example: 1→×1111→×61671→+1672→×320161\overset{{\times 11}}{\to}11 \overset{{\times 61}}{\to} 671 \overset{{+1}}{\to}672 \overset{{\times 3}}{\to}2016 How many Lusophone sequences exist in which (as in the example above) the add 11 operation was used exactly once and not multiplied twice by the same prime number?
number theoryprime numbersprimeSequence