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

Author

Antonia Münchenbach, Jan 25 2016

Keywords

• nonn
• base
• fini
• full

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).

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..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

Crossrefs

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