A276273 Replacing every "mixed pair" of integers (as defined in the comments) with the smaller integer of the pair rebuilds the sequence.

1, 2, 2, 3, 3, 2, 4, 3, 3, 4, 2, 3, 5, 4, 4, 3, 3, 4, 4, 5, 3, 2, 4, 3, 5, 6, 4, 5, 5, 4, 4, 3, 3, 4, 4, 5, 5, 4, 6, 5, 3, 4, 2, 3, 5, 4, 4, 3, 5, 6, 6, 7, 5, 4, 6, 5, 5, 6, 4, 5, 5, 4, 4, 3, 3, 4, 4, 5, 5, 4, 6, 5, 5, 6, 4, 5, 7, 6, 6, 5, 3, 4, 4, 5, 3, 2, 4, 3, 5, 6, 4, 5, 5, 4, 4, 3, 5, 6, 6, 7, 7, 6, 8, 7, 5, 6, 4, 5, 7, 6, 6, 5, 5, 6, 6, 7, 5, 4, 6, 5, 5, 6, 4, 5, 5, 4, 4, 3, 3, 4, 4

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Aug 26 2016

Keywords

• nonn
• base
• easy

Comments

A "mixed pair" is a pair of successive integers that add to an odd number.

By definition, the sequence has the repeated pattern oeeo (odd-even-even-odd integers) and starts with a(1) = 1. It is always extended with the smallest integer not leading to a contradiction.

Every natural number will appear in the sequence - but very slowly: the biggest integer after 200000 terms is still 18!

Examples

			The "mixed pairs" in the sequence are between parentheses:
(1,2),(2,3),(3,2),(4,3),(3,4),(2,3),(5,4),(4,3),...
Replacing the content of the parentheses by their smallest term gives (1),(2),(2),(3),(3),(2),(4),(3),...
which is indeed the starting sequence.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..10004

Crossrefs

Cf. A000120, A064706.

Formula

It seems a(n) = A000120(A064706(n-1)) + 1. - Peter Munn, Aug 12 2023

Extensions

Name edited by Peter Munn, Aug 12 2023