OFFSET
1,1
COMMENTS
The T operator numerically summarizes the frequency of digits 0 through 6 in that order when they occur in a number. The numbers and the frequency are written in base 7.
These are all autobiographical numbers in base 7 which lead to a fixed-point or belong to a cycle.
There are three cycles with length 2 (103142132415 /104122232415, 103142132416/104122232416, 314213241516/412223241516), one cycle with length 3 (10512213341516/10512223142516/10414213142516). 29 numbers are fixed-points.
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
10213223 contains one 0, two 1's, three 2's and two 3's, so T(10213223) = 1 0 2 1 3 2 2 3, and this is fixed under T.
103142132415 and 104122232415 belong to the cycle of length 2, so
T(T(103142132415)) = T(1 0 4 1 2 2 2 3 2 4 1 5) = 1 0 3 1 4 2 1 3 2 4 1 5.
CROSSREFS
KEYWORD
nonn,base,fini,full
AUTHOR
Antonia Münchenbach, Jan 16 2016
STATUS
approved