A267499 - OEIS

%I #23 Dec 19 2017 17:30:03

%S 2,7,7,12,19,29,44,68,109,183

%N Number of fixed points of autobiographical numbers (A267491 ... A267498) in base n.

%C For n>=5, it seems that a(n)=2^(n-4)+1/2*n^2-1/2*n describes the number of fixed points in base n. The formula is correct for 5<=n<=11, but unknown for n>11. We assume it's correct for all n>=5.

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

%F a(n)=2^(n-4)+1/2*n^2-1/2*n for 5<=n<=11, unknown for n>11.

%e In base two there are only two fixed-points, 111 and 1101001.

%e In base 3, there are 7 fixed-points: 22, 10111, 11112, 100101, 1011122, 2021102, and 10010122.

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

%K nonn,base,more

%O 2,1

%A _Antonia Münchenbach_, Jan 16 2016