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A144783 Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 10. 15
10, 91, 8191, 67084291, 4500302031888391, 20252718378218776104731448680491, 410172601707440572557971589875869064610540321970215293555320591, 168241563191450680898537024308131628447885486994777537422995633998657738457104605412468520116391629012196009150161991233268691 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
REFERENCES
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
LINKS
FORMULA
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.
MATHEMATICA
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 *)
NestList[#^2-#+1&, 10, 8] (* Harvey P. Dale, May 07 2017 *)
CROSSREFS
Sequence in context: A267833 A354380 A015467 * A365217 A227512 A227513
KEYWORD
nonn
AUTHOR
Artur Jasinski, Sep 21 2008
STATUS
approved

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)