[seqfan] 3 -colouring of N

michel.marcus at free.fr michel.marcus at free.fr
Sun May 20 11:46:30 CEST 2018


Dear Seqfans, 


Yesterday I was having a look at Peter Cameron's blog at https://cameroncounts.wordpress.com/2018/05/11/london-combinatorics-colloquia-3/ 
The "After lunch" paragraph led me to https://arxiv.org/abs/1608.08374 


Assuming I understood correctly, I wrote this pari script c(i) = if (i < 3, i, setminus([0,1,2], [c(i\2), c(i\2+1)])[1]) \\ note the [1] (first available colour) 
then for (n=0, 30, print1(c(n), ", ")) gives with output 0, 1, 2, 0, 0, 0, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, ... 


But it appears that in some cases, there are 2 choices for the new c(i). 
cp(i) = if (i < 3, i, v = setminus([0,1,2], [cp(i\2), cp(i\2+1)]); print1(#v, ", "); v[1]); \\ quick and dirty 
then for (n=0, 30, cp(n)) gives 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, .... 


So, unless mistaken, we have several c(i) sequences, what can we do from here to enter something in OEIS ? 
Best. 



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