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

Source: Lusophon 2016 CPLP P5

August 29, 2018
number theoryprime numbersprimeSequence

Problem Statement

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?
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