A267496 - OEIS

%I #25 Dec 19 2017 18:36:34

%S 22,10213223,10311233,10313314,10313315,10313316,10313317,21322314,

%T 21322315,21322316,21322317,31123314,31123315,31123316,31123317,

%U 31331415,31331416,31331417,31331516,31331517,31331617

%N Autobiographical numbers in base 8: 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 7 in that order when they occur in a number. The numbers and the frequency are written in base 8.

%C These are all autobiographical numbers in base 8 which lead to a fixed-point or belong to a cycle.

%C 44 numbers are fixed-points. There are 7 cycles with length 2 and three cycles with length 3.

%D Antonia Münchenbach and Nicole Anton George, "Eine Abwandlung der Conway-Folge", contribution to "Jugend forscht" 2016, 2016

%H Antonia Münchenbach, <a href="/A267496/b267496.txt">Table of n, a(n) for n = 1..67</a>

%H Andre Kowacs, <a href="https://arxiv.org/abs/1708.06452">Studies on the Pea Pattern Sequence</a>, arXiv:1708.06452 [math.HO], 2017.

%H Antonia Münchenbach, <a href="/A267496/a267496.txt">Numbers sorted as fixed-points, cycles with length 2 and 3</a>

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

%K nonn,base,fini,full

%O 1,1

%A _Antonia Münchenbach_, Jan 16 2016