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A329949 Lexicographically earliest sequence of positive numbers such that following proposition is true: a(n) is the number of occurrences of a(n+1) in the sequence so far, up to and including a(n+1). 0

%I

%S 1,2,2,1,3,2,3,3,1,4,2,4,3,4,4,1,5,2,5,3,5,4,5,5,1,6,2,6,3,6,4,6,5,6,

%T 6,1,7,2,7,3,7,4,7,5,7,6,7,7,1,8,2,8,3,8,4,8,5,8,6,8,7,8,8,1,9,2,9,3,

%U 9,4,9,5,9,6,9,7,9,8,9,9,1,10,2,10,3,10,4,10,5,10,6,10,7,10,8,10,9,10,10,1,11,2,11,3,11,4,11,5,11,6,11,7,11,8,11,9,11,10,11,11,1,12

%N Lexicographically earliest sequence of positive numbers such that following proposition is true: a(n) is the number of occurrences of a(n+1) in the sequence so far, up to and including a(n+1).

%C It is easy to see how regular the sequence is by transforming it into a triangle with 2k+1 terms in each row, where k runs through the natural numbers. Then one sees that a(k^2) = 1, a(k^2 + 1) = k+1 etc. - _Ivan N. Ianakiev_, Nov 26 2019

%e a(1) = 1 means that there is 1 a(2) so far in the sequence - which is true, there is one "2" in the sequence up to a(2);

%e a(2) = 2 means that there are 2 a(3) so far in the sequence - which is true, there are two "2" in the sequence up to a(3);

%e a(3) = 2 means that there are 2 a(4) so far in the sequence - which is true, there are two "1" in the sequence up to a(4);

%e a(4) = 1 means that there is 1 a(4) so far in the sequence - which is true, there is one "3" in the sequence up to a(5);

%e a(5) = 3 means that there are 3 a(6) so far in the sequence - which is true, there are three "2" in the sequence up to a(6); etc.

%K base,nonn

%O 1,2

%A _Eric Angelini_, Nov 25 2019

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Last modified October 24 10:03 EDT 2021. Contains 348225 sequences. (Running on oeis4.)