OFFSET
1,1
COMMENTS
Only seven such numbers are known. Referring to A204539, we cannot be certain that these are the only numbers k with the property basin(k) = 1, but there are no others for k less than 12,000,000. Furthermore the average value of basin(k) is approximately equal to k/3 for large values of k, which makes it extremely unlikely that another one will ever be found.
For unknown reasons, all integers > 5 with basin equal to 1 or 2 are even. See A185001 for the list of known numbers with basin = 2.
LINKS
Mark Dukes, Fagan's Construction, Strange Roots, and Tchoukaillon Solitaire, Journal of Integer Sequences, Vol. 24 (2021), Article 21.7.1.
Mark Dukes, Fagan's Construction, Strange Roots, and Tchoukaillon Solitaire, arXiv:2202.02381 [math.NT], 2022.
MATHEMATICA
(* First run the program for A204539 to define basin *) Select[Range[1000], basin[#] == 1 &]] (* Alonso del Arte, Jan 19 2012 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Colm Fagan, Jan 16 2012
STATUS
approved