cp's OEIS Frontend

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

%I A267497 #23 Dec 19 2017 18:36:41
%S A267497 22,10213223,10311233,10313314,10313315,10313316,10313317,10313318,
%T A267497 21322314,21322315,21322316,21322317,21322318,31123314,31123315,
%U A267497 31123316,31123317,31123318
%N A267497 Autobiographical numbers in base 9: numbers which are fixed or belong to a cycle under the operator T (see comments).
%C A267497 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.
%C A267497 These are all autobiographical numbers in base 9 which lead to a fixed-point or belong to a cycle.
%C A267497 68 numbers are fixed-points. There are 15 cycles with length 2 and 6 cycles with length 3.
%D A267497 Antonia Münchenbach and Nicole Anton George, "Eine Abwandlung der Conway-Folge", contribution to "Jugend forscht" 2016, 2016
%H A267497 Antonia Münchenbach, <a href="/A267497/b267497.txt">Table of n, a(n) for n = 1..116</a>
%H A267497 Andre Kowacs, <a href="https://arxiv.org/abs/1708.06452">Studies on the Pea Pattern Sequence</a>, arXiv:1708.06452 [math.HO], 2017.
%H A267497 Antonia Münchenbach, <a href="/A267497/a267497.txt">Numbers sorted as fixed-points, cycles with length 2 and 3</a>
%e A267497 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.
%e A267497 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.
%Y A267497 Cf. A047841, A267491, A267492, A267493, A267494, A267495, A267496, A267497, A267498, A267499, A267500, A267502.
%K A267497 nonn,base,fini,full
%O A267497 1,1
%A A267497 _Antonia Münchenbach_, Jan 23 2016