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A267491 Autobiographical numbers in base 3: numbers which are fixed or belong to a cycle under the operator T. 11
22, 10111, 11112, 100101, 1011122, 2012112, 2021102, 10010122, 10011112, 10101102 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A202054 A279298 A235389 * A013727 A370314 A229346
KEYWORD
nonn,base,full,fini
AUTHOR
STATUS
approved

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Last modified June 17 21:09 EDT 2024. Contains 373464 sequences. (Running on oeis4.)