|
%I #16 Dec 19 2017 18:36:14
%S 22,1011112,1011113,1111213,10311233,101112213
%N Autobiographical numbers in base 4: numbers which are fixed or belong to a cycle under the operator T.
%C The T operator numerically summarizes the frequency of digits 0 through 3 in that order when they occur in a number. The numbers and the frequency are written in base 4.
%C These are all autobiographical numbers in base 4 which lead to a fixed-point or belong to a cycle. However, in base 4 there are no cycles of length greater than 1, that is, all the terms are fixed-points.
%D Antonia Münchenbach and Nicole Anton George, "Eine Abwandlung der Conway-Folge", contribution to "Jugend forscht", 2016
%H Andre Kowacs, <a href="https://arxiv.org/abs/1708.06452">Studies on the Pea Pattern Sequence</a>, arXiv:1708.06452 [math.HO], 2017.
%e 1011112 contains one 0, five (11 in base 4) 1's, and one 2, so T(1011112) = 1 0 11 1 1 2, and this is fixed under T.
%Y Cf. A047841, A267491.
%K nonn,base,fini,full
%O 1,1
%A _Antonia Münchenbach_, Jan 16 2016
|
