OFFSET
1,1
COMMENTS
The T operator numerically summarizes the frequency of digits 0 through 2 in that order when they occur in a number. The numbers and the frequency are written in base 3.
These are all autobiographical numbers in base 3 which lead to a fixed-point or belong to a cycle. However, in base 3 there is only one cycle with length 3, all other terms are fixed-points.
10011112, 10101102, 2012112 is a cycle of length 3, which means T(10011112)=10101102, T(10101102)=2012112, T(2012112)=10011112.
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.
EXAMPLE
11112 contains four 1's (11 in base 3), and one 2, so T(11112) = 11 1 1 2, and so 11112 is fixed under T.
CROSSREFS
KEYWORD
nonn,base,full,fini
AUTHOR
Antonia Münchenbach, Jan 16 2016
STATUS
approved