A267497 Autobiographical numbers in base 9: numbers which are fixed or belong to a cycle under the operator T (see comments).

22, 10213223, 10311233, 10313314, 10313315, 10313316, 10313317, 10313318, 21322314, 21322315, 21322316, 21322317, 21322318, 31123314, 31123315, 31123316, 31123317, 31123318

Offset

1,1

Comments

The T operator numerically summarizes the frequency of digits 0 through 8 in that order when if occur in a number. The frequency and the numbers are written in base 9.

These are all autobiographical numbers in base 9 which lead to a fixed-point or belong to a cycle.

68 numbers are fixed-points. There are 15 cycles with length 2 and 6 cycles with length 3.

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..116

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

Example

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.

Crossrefs

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

Sequence in context: A173101 A047841 A267498 * A267496 A267495 A267494

Adjacent sequences: A267494 A267495 A267496 * A267498 A267499 A267500

Keyword

nonn,base,fini,full

Author

Antonia Münchenbach, Jan 23 2016

Status

approved