A267494 Autobiographical numbers in base 6: numbers which are fixed or belong to a cycle under the operator T.

22, 10213223, 10311233, 10313314, 10313315, 21322314, 21322315, 31123314, 31123315, 31331415, 1031223314, 1031223315, 3122331415, 10111121314, 10111121315, 10111121415, 10111131415, 11112131415, 103142132415, 104122232415, 1011122131415

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 5 in that order when they occur in a number. The numbers and the frequency are written in base 6.

These are all autobiographical numbers in base 6 which lead to a fixed-point or belong to a cycle.

There is one cycle with length 2 (103142132415, 104122232415), all other numbers are fixed-points.

Examples

			10213223 contains one 0, two 1's, three 2's and two 3's, so T(10213223) = 1 0 2 1 3 2 2 3, and this is fixed under T.
103142132415 and 104122232415 belong to the cycle of length 2, so
T(T(103142132415)) = T(1 0 4 1 2 2 2 3 2 4 1 5) = 1 0 3 1 4 2 1 3 2 4 1 5.
		

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.