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

1,1

Links

Table of n, a(n) for n=1..8.

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.

Formula

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

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 *)

Crossrefs

Cf. A000058, A082732, A144805.

Sequence in context: A324205 A002402 A015464 * A026948 A111585 A055839

Adjacent sequences: A144778 A144779 A144780 * A144782 A144783 A144784

Keyword

nonn

Author

Artur Jasinski, Sep 21 2008

Status

approved