This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A276273 #15 Aug 12 2023 08:54:06 %S A276273 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, %T A276273 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, %U A276273 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 %N A276273 Replacing every "mixed pair" of integers (as defined in the comments) with the smaller integer of the pair rebuilds the sequence. %C A276273 A "mixed pair" is a pair of successive integers that add to an odd number. %C A276273 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. %C A276273 Every natural number will appear in the sequence - but very slowly: the biggest integer after 200000 terms is still 18! %H A276273 Jean-Marc Falcoz, <a href="/A276273/b276273.txt">Table of n, a(n) for n = 1..10004</a> %F A276273 It seems a(n) = A000120(A064706(n-1)) + 1. - _Peter Munn_, Aug 12 2023 %e A276273 The "mixed pairs" in the sequence are between parentheses: %e A276273 (1,2),(2,3),(3,2),(4,3),(3,4),(2,3),(5,4),(4,3),... %e A276273 Replacing the content of the parentheses by their smallest term gives (1),(2),(2),(3),(3),(2),(4),(3),... %e A276273 which is indeed the starting sequence. %Y A276273 Cf. A000120, A064706. %K A276273 nonn,base,easy %O A276273 1,2 %A A276273 _Eric Angelini_ and _Jean-Marc Falcoz_, Aug 26 2016 %E A276273 Name edited by _Peter Munn_, Aug 12 2023