OFFSET
1,1
COMMENTS
The T operator numerically summarizes the frequency of digits 0 through 8 in that order when if occur in a number. The frequency and the numbers are written in base 9.
These are all autobiographical numbers in base 9 which lead to a fixed-point or belong to a cycle.
68 numbers are fixed-points. There are 15 cycles with length 2 and 6 cycles with length 3.
REFERENCES
Antonia Münchenbach and Nicole Anton George, "Eine Abwandlung der Conway-Folge", contribution to "Jugend forscht" 2016, 2016
LINKS
Antonia Münchenbach, Table of n, a(n) for n = 1..116
Andre Kowacs, Studies on the Pea Pattern Sequence, arXiv:1708.06452 [math.HO], 2017.
Antonia Münchenbach, Numbers sorted as fixed-points, cycles with length 2 and 3
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 23 2016
STATUS
approved