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%I #21 Mar 16 2018 05:21:14
%S 0,3,0,0,0,3,9,18,45
%N Number of cycles of length 3 of autobiographical numbers (A267491 ... A267498) in base n.
%C a(n) is the number of cycles of length 3 of autobiographical numbers in base n. For n>=5, it seems that a(n)=3/2*n^2-33/2*n+45 describes the number of cycles of length 3 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
%F Conjecture: a(n) = 3/2*n^2 - 33/2*n + 45. The formula is correct for 5<=n<=11, but unknown for n>11. We assume it's correct for all n>=5.
%e In base two, four, five and six there is no cycle of length 3.
%e In base three, there is 1 cycle of length 3 with 3 numbers: 10011112, 10101102, 2012112.
%e In base 10, there are 6 cycles of length 3 (18 numbers).
%Y Cf. A047841, A267491, A267492, A267493, A267494, A267495, A267496, A267497, A267498, A267499, A267500, A267501, A267502.
%K nonn,base,more
%O 2,2
%A _Antonia Münchenbach_, Jan 28 2016
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