%I #18 Jan 15 2021 21:09:09
%S 10,91,8191,67084291,4500302031888391,
%T 20252718378218776104731448680491,
%U 410172601707440572557971589875869064610540321970215293555320591,168241563191450680898537024308131628447885486994777537422995633998657738457104605412468520116391629012196009150161991233268691
%N Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 10.
%D 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
%F a(n) = round((3.08435104906918990233569320020272148875011089837398848476442237096569...)^(2^n)) = round(A144807^(2^n)). [corrected by _Joerg Arndt_, Jan 15 2021]
%F a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 10.
%t a = {}; r = 10; Do[AppendTo[a, r]; r = r^2 - r + 1, {n, 1, 10}]; a (* or *)
%t Table[Round[3.08435104906918990233569320020272148875011089837398848476442237096569188195734783139337492942278549518507672786196650938869338548385641623^(2^n)], {n, 1, 8}] (* _Artur Jasinski_ *)
%t NestList[#^2-#+1&,10,8] (* _Harvey P. Dale_, May 07 2017 *)
%Y Cf. A000058, A082732, A144779, A144780, A144781, A144782, A144783, A144784, A144785, A144786, A144787, A144788.
%K nonn
%O 1,1
%A _Artur Jasinski_, Sep 21 2008