"A Handbook of Integer Sequences" Fifty Years Later.

Gijswijt's Sequence (A090822) For this sequence, it will be helpful to remember that chemists do not write HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">HHO</mi></math> ht for water; they write HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi></mrow></math> ht . So the sequence with a single term 99, say, can be written as HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Y</mi><mn>1</mn></msup></math> ht , where I Y i is the number 99, and it has curling number 1. If you think of an animal with its head looking to the left, with a very curly tail, then I X i represents the head and body of the animal, and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Y</mi><mi>k</mi></msup></math> ht represents the curls in its tail. The case of an HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></math> ht grid seems even harder. [Extracted from the article]