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Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 12
15

%I #7 Jan 01 2016 10:36:52

%S 12,133,17557,308230693,95006159799029557,

%T 9026170399758739819525199160586693,

%U 81471752085480849000657595909467634426991447160798281416700808089557

%N Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 12

%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) =3.39277252592669675143137065018187376847206615308598784654603692312172475924599026837940758013759324881455503678006543568111163817496672898^(2^n) a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 11

%t a = {}; r = 12; Do[AppendTo[a, r]; r = r^2 - r + 1, {n, 1, 10}]; a or Table[Round[3.39277252592669675143137065018187376847206615308598784654603692312172475924599026837940758013759324881455503678006543568111163817496672898^(2^n)], {n, 1, 8}] (*Artur Jasinski*)

%t NestList[#^2-#+1&,12,6] (* _Harvey P. Dale_, Jan 01 2016 *)

%Y A000058, A082732, A144779, A144780, A144781, A144782, A144783, A144784, A144785, A144786, A144787, A144788

%K nonn

%O 1,1

%A _Artur Jasinski_, Sep 21 2008