A267499 Number of fixed points of autobiographical numbers (A267491 ... A267498) in base n.

2, 7, 7, 12, 19, 29, 44, 68, 109, 183

Offset: 2

Author

Antonia Münchenbach, Jan 16 2016

Keywords

• nonn
• base
• more

Comments

For n>=5, it seems that a(n)=2^(n-4)+1/2*n^2-1/2*n describes the number of fixed points in base n. The formula is correct for 5<=n<=11, but unknown for n>11. We assume it's correct for all n>=5.

Examples

			In base two there are only two fixed-points, 111 and 1101001.
In base 3, there are 7 fixed-points: 22, 10111, 11112, 100101, 1011122, 2021102, and 10010122.
		

References

• Antonia Münchenbach and Nicole Anton George, "Eine Abwandlung der Conway-Folge", contribution to "Jugend forscht" 2016, 2016.

Links

• Andre Kowacs, Studies on the Pea Pattern Sequence, arXiv:1708.06452 [math.HO], 2017.

Crossrefs

Cf. A047841, A267491, A267492, A267493, A267494, A267495, A267496, A267497, A267498, A267499, A267500, A267502.

Formula

a(n)=2^(n-4)+1/2*n^2-1/2*n for 5<=n<=11, unknown for n>11.