A267491 Autobiographical numbers in base 3: numbers which are fixed or belong to a cycle under the operator T.

22, 10111, 11112, 100101, 1011122, 2012112, 2021102, 10010122, 10011112, 10101102

Offset: 1

Author

Antonia Münchenbach, Jan 16 2016

Keywords

• nonn
• base
• full
• fini

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.

Examples

			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.
		

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.

Crossrefs

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