A267496 Autobiographical numbers in base 8: numbers which are fixed or belong to a cycle under the operator T.

22, 10213223, 10311233, 10313314, 10313315, 10313316, 10313317, 21322314, 21322315, 21322316, 21322317, 31123314, 31123315, 31123316, 31123317, 31331415, 31331416, 31331417, 31331516, 31331517, 31331617

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 7 in that order when they occur in a number. The numbers and the frequency are written in base 8.

These are all autobiographical numbers in base 8 which lead to a fixed-point or belong to a cycle.

44 numbers are fixed-points. There are 7 cycles with length 2 and three cycles with length 3.

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

• Antonia Münchenbach, Table of n, a(n) for n = 1..67
• Andre Kowacs, Studies on the Pea Pattern Sequence, arXiv:1708.06452 [math.HO], 2017.
• Antonia Münchenbach, Numbers sorted as fixed-points, cycles with length 2 and 3

Crossrefs

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