OFFSET
2,1
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.
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.
FORMULA
a(n)=2^(n-4)+1/2*n^2-1/2*n for 5<=n<=11, unknown for 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, and 10010122.
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Antonia Münchenbach, Jan 16 2016
STATUS
approved