A185001 Numbers k with the property that their basins (as defined in A204539) are 2.

5, 8, 10, 16, 22, 26, 106, 110, 182, 234, 282, 288, 318, 434, 766, 1056, 1072, 1462, 1550, 1930, 3024, 4330, 5424, 9398, 10634, 53094, 90602, 151632, 384002, 511638, 530102, 1364850, 1887006, 2193072, 3138096, 6470672, 6959070

Offset: 1

Author

Colm Fagan, Jan 23 2012

Keywords

• nonn
• more

Comments

This sequence follows on from A204540, which lists seven values of k for which basin(k) = 1. There are 37 known values of k for which basin(k) = 2. A search of numbers up to 10,000,000 has not uncovered any further integers with this property. The possibility that there are even larger numbers with basins equal to 2 cannot be completely ruled out, but the chances of one being discovered are remote, in view of the fact that the average basin size for large values of k is approximately k/3, that is, over 2000000 in the region where the last known such integer was discovered.

For unknown reasons, all integers > 5 with basins equal to 1 or 2 are even.

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, A204540.