A144781 Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 8.

8, 57, 3193, 10192057, 103878015699193, 10790642145601683494645152057, 116437957914435303575899742229333045108448631998006179193, 13557798043283806950297045269968250387897834581711367551819275131055206893868524458302302046950954641412419952057

Offset: 1

Author

Artur Jasinski, Sep 21 2008

Keywords

• nonn

Links

• 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.
• Mohammad K. Azarian, Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Solution College Mathematics Journal, Vol. 43, No. 4, September 2012, pp. 340-342.

Crossrefs

Cf. A000058, A082732, A144805.

Programs

Mathematica

a = {}; k = 8; Do[AppendTo[a, k]; k = k^2 - k + 1, {n, 1, 10}]; a
NestList[#^2-#+1&,8,10] (* Harvey P. Dale, Jan 29 2017 *)

Formula

a(n) ~ c^(2^n) where is c is 2.74167747444233776776... (A144805).