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

1,2

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!

Links

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

Formula

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

Example

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.

Crossrefs

Cf. A000120, A064706.

Sequence in context: A234399 A214749 A239330 * A039643 A288887 A154258

Adjacent sequences: A276270 A276271 A276272 * A276274 A276275 A276276

Keyword

nonn,base,easy

Author

Eric Angelini and Jean-Marc Falcoz, Aug 26 2016

Extensions

Name edited by Peter Munn, Aug 12 2023

Status

approved