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).

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, 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, 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

Offset: 1

Author

Eric Angelini, Nov 25 2019

Keywords

• base
• nonn

Comments

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

Examples

			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);
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);
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);
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);
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.
		

Crossrefs

Cf. A349526