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

2,1

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.

References

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

Links

Table of n, a(n) for n=2..11.

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

Formula

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

Example

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).

Crossrefs

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

Sequence in context: A213135 A037187 A248061 * A355785 A300016 A368559

Adjacent sequences: A267497 A267498 A267499 * A267501 A267502 A267503

Keyword

nonn,base,more

Author

Antonia Münchenbach, Jan 27 2016

Status

approved