A267492 Autobiographical numbers in base 4: numbers which are fixed or belong to a cycle under the operator T.

22, 1011112, 1011113, 1111213, 10311233, 101112213

Offset: 1

Author

Antonia Münchenbach, Jan 16 2016

Keywords

• nonn
• base
• fini
• full

Comments

The T operator numerically summarizes the frequency of digits 0 through 3 in that order when they occur in a number. The numbers and the frequency are written in base 4.

These are all autobiographical numbers in base 4 which lead to a fixed-point or belong to a cycle. However, in base 4 there are no cycles of length greater than 1, that is, all the terms are fixed-points.

Examples

			1011112 contains one 0, five (11 in base 4) 1's, and one 2, so T(1011112) = 1 0 11 1 1 2, and this is fixed under T.
		

References

• Antonia Münchenbach and Nicole Anton George, "Eine Abwandlung der Conway-Folge", contribution to "Jugend forscht", 2016

Links

• Andre Kowacs, Studies on the Pea Pattern Sequence, arXiv:1708.06452 [math.HO], 2017.

Crossrefs

Cf. A047841, A267491.