A267500 Number of fixed points or cycles of autobiographical numbers (A267491 ... A267498) in base n.

2, 10, 7, 12, 21, 38, 67, 116, 201, 354

Offset: 2

Author

Antonia Münchenbach, Jan 27 2016

Keywords

• nonn
• base
• more

Comments

For n>=5, it appears that a(n)=2^(n-3)+2*n^2-17*n+43. This formula is correct for 5<=n<=11, but may not be true for larger n.

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, 10010122 and 1 cycle of length 3 with 2012112, 1010102, 10011112.
In base 10, there are 109 fixed-points, 31 cycles of length 2 (62 numbers) and 10 cycles of length 3 (30 numbers).
		

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-3) + 2*n^2 - 17*n + 43, for 5<=n<=11.