A204540 Numbers k whose basins (as defined in A204539) equal 1.

2, 3, 4, 6, 14, 1760, 39046

Offset: 1

Author

Colm Fagan, Jan 16 2012

Keywords

• nonn
• more

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.

Crossrefs

Cf. A204539, A185001.

Programs

Mathematica

(* First run the program for A204539 to define basin *) Select[Range[1000], basin[#] == 1 &] (* Alonso del Arte, Jan 19 2012 *)