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A267499
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Number of fixed points of autobiographical numbers (A267491 ... A267498) in base n.
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10
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OFFSET
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2,1
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COMMENTS
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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.
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REFERENCES
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Antonia Münchenbach and Nicole Anton George, "Eine Abwandlung der Conway-Folge", contribution to "Jugend forscht" 2016, 2016.
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LINKS
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FORMULA
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a(n)=2^(n-4)+1/2*n^2-1/2*n for 5<=n<=11, unknown for n>11.
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EXAMPLE
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In base two there are only two fixed-points, 111 and 1101001.
In base 3, there are 7 fixed-points: 22, 10111, 11112, 100101, 1011122, 2021102, and 10010122.
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CROSSREFS
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Cf. A047841, A267491, A267492, A267493, A267494, A267495, A267496, A267497, A267498, A267499, A267500, A267502.
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KEYWORD
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nonn,base,more
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AUTHOR
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STATUS
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approved
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