A267502 Number of cycles of length 3 of autobiographical numbers (A267491 ... A267498) in base n.

0, 3, 0, 0, 0, 3, 9, 18, 45

Offset

2,2

Comments

a(n) is the number of cycles of length 3 of autobiographical numbers in base n. For n>=5, it seems that a(n)=3/2*n^2-33/2*n+45 describes the number of cycles of length 3 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.

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..10.

Formula

Conjecture: a(n) = 3/2*n^2 - 33/2*n + 45. The formula is correct for 5<=n<=11, but unknown for n>11. We assume it's correct for all n>=5.

Example

In base two, four, five and six there is no cycle of length 3.
In base three, there is 1 cycle of length 3 with 3 numbers:  10011112, 10101102, 2012112.
In base 10, there are 6 cycles of length 3 (18 numbers).

Crossrefs

Cf. A047841, A267491, A267492, A267493, A267494, A267495, A267496, A267497, A267498, A267499, A267500, A267501, A267502.

Sequence in context: A007514 A336642 A151671 * A296605 A354488 A278478

Adjacent sequences: A267499 A267500 A267501 * A267503 A267504 A267505

Keyword

nonn,base,more

Author

Antonia Münchenbach, Jan 28 2016

Status

approved