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A144783
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Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 10.
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15
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10, 91, 8191, 67084291, 4500302031888391, 20252718378218776104731448680491, 410172601707440572557971589875869064610540321970215293555320591, 168241563191450680898537024308131628447885486994777537422995633998657738457104605412468520116391629012196009150161991233268691
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OFFSET
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1,1
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REFERENCES
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Mohammad K. Azarian, Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330. Solution published in Vol. 43, No. 4, September 2012, pp. 340-342
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LINKS
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FORMULA
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a(n) = round((3.08435104906918990233569320020272148875011089837398848476442237096569...)^(2^n)) = round(A144807^(2^n)). [corrected by Joerg Arndt, Jan 15 2021]
a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 10.
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MATHEMATICA
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a = {}; r = 10; Do[AppendTo[a, r]; r = r^2 - r + 1, {n, 1, 10}]; a (* or *)
Table[Round[3.08435104906918990233569320020272148875011089837398848476442237096569188195734783139337492942278549518507672786196650938869338548385641623^(2^n)], {n, 1, 8}] (* Artur Jasinski *)
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CROSSREFS
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Cf. A000058, A082732, A144779, A144780, A144781, A144782, A144783, A144784, A144785, A144786, A144787, A144788.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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