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%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