A144784 Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 11.

11, 111, 12211, 149096311, 22229709804712411, 494159998001727075769152612720511, 244194103625066907517263589918036880566782292998362610615987380611

Offset

1,1

Comments

For the "exact" formula, compare the Aho-Sloane reference in A000058. - N. J. A. Sloane, Apr 07 2014

Links

Table of n, a(n) for n=1..7.

A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.

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

a(n) ~ c^(2^n) where c = 3.242214... (see A144808).

Mathematica

a = {}; r = 11; Do[AppendTo[a, r]; r = r^2 - r + 1, {n, 1, 10}]; a

Crossrefs

Cf. A000058, A082732, A144779, A144780, A144781, A144782, A144783, A144784, A144785, A144786, A144787, A144788, A144808.

See A239900 for another version.

Sequence in context: A037842 A131293 A108047 * A030175 A263805 A058949

Adjacent sequences: A144781 A144782 A144783 * A144785 A144786 A144787

Keyword

nonn

Author

Artur Jasinski, Sep 21 2008

Status

approved