

A267491


Autobiographical numbers in base 3: numbers which are fixed or belong to a cycle under the operator T.


11




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 fixedpoint or belong to a cycle. However, in base 3 there is only one cycle with length 3, all other terms are fixedpoints.
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 ConwayFolge", contribution to "Jugend forscht" 2016, 2016


LINKS



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

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


KEYWORD

nonn,base,full,fini


AUTHOR



STATUS

approved



