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MMO 282 Moscow MO 1954 sequence 1, 0, 3, 6, 9, 4, 7, 2, 5, 8, 8, 5, 10, 13, 13

Source:

August 13, 2019
SequenceInteger sequencealgebra

Problem Statement

Given a sequence of numbers a1,a2,...,a15a_1, a_2, ..., a_{15}, one can always construct a new sequence b1,b2,...,b15b_1,b_2, ..., b_{15}, where bib_i is equal to the number of terms in the sequence {ak}k=115\{a_k\}^{15}_{k=1} less than aia_i (i=1,2,...,15i = 1, 2,..., 15). Is there a sequence {ak}k=115\{a_k\}^{15}_{k=1} for which the sequence {bk}k=115\{b_k\}^{15}_{k=1} is 1,0,3,6,9,4,7,2,5,8,8,5,10,13,13 ?1, 0, 3, 6, 9, 4, 7, 2, 5, 8, 8, 5, 10, 13, 13 \,?
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