A267493 Autobiographical numbers in base 5: numbers which are fixed or belong to a cycle under the operator T.

22, 10213223, 10313314, 10311233, 21322314, 31123314, 101111314, 101111213, 101111214, 111121314, 1031223314, 10111221314

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 4 in that order when they occur in a number. The numbers and the frequency are written in base 5.

These are all autobiographical numbers in base 5 which lead to a fixed-point or belong to a cycle. However, in base 5 there are no cycles of length greater than 1, that is, all the terms are fixed-points.

Examples

			10213223 contains 1 0's, 2 1's, 3 2's and 2 3's.
		

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, A047842.

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