A144785 Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 12.

12, 133, 17557, 308230693, 95006159799029557, 9026170399758739819525199160586693, 81471752085480849000657595909467634426991447160798281416700808089557

Offset: 1

Author

Artur Jasinski, Sep 21 2008

Keywords

• nonn

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

Crossrefs

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

Programs

Mathematica

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*)
NestList[#^2-#+1&,12,6] (* Harvey P. Dale, Jan 01 2016 *)

Formula

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