A267498 Autobiographical numbers in base 10: numbers which are fixed or belong to a cycle under the operator T.

22, 10213223, 10311233, 10313314, 10313315, 10313316, 10313317, 10313318, 10313319, 21322314, 21322315, 21322316, 21322317, 21322318, 21322319, 31123314, 31123315, 31123316, 31123317, 31123318, 31123319, 31331415, 31331416, 31331417, 31331418, 31331419, 31331516, 31331517, 31331518

Offset

1,1

Comments

The T operator numerically summarizes the frequency of digits 0 through 9 in that order when they occur in a number. The numbers and the frequency are written in base 10.

These are all autobiographical numbers in base 10 which lead to a fixed-point or belong to a cycle.

109 numbers are fixed-points. There are 31 cycles with length 2 (62 numbers) and 10 cycles with length 3 (30 numbers).

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..201

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: A104789 A173101 A047841 * A267497 A267496 A267495

Adjacent sequences: A267495 A267496 A267497 * A267499 A267500 A267501

Keyword

nonn,base,fini,full

Author

Antonia Münchenbach, Jan 25 2016

Status

approved