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A267500 Number of fixed points or cycles of autobiographical numbers (A267491 ... A267498) in base n. 10

%I #23 Dec 19 2017 18:36:53

%S 2,10,7,12,21,38,67,116,201,354

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

%C For n>=5, it appears that a(n)=2^(n-3)+2*n^2-17*n+43. This formula is correct for 5<=n<=11, but may not be true for larger n.

%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-3) + 2*n^2 - 17*n + 43, for 5<=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, 10010122 and 1 cycle of length 3 with 2012112, 1010102, 10011112.

%e In base 10, there are 109 fixed-points, 31 cycles of length 2 (62 numbers) and 10 cycles of length 3 (30 numbers).

%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 27 2016

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Last modified March 28 07:20 EDT 2024. Contains 371235 sequences. (Running on oeis4.)