A144782 Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 9.

9, 73, 5257, 27630793, 763460694178057, 582872231554839914154126117193, 339740038317718918529575265905277902175236102890836244082057

Offset

1,1

Links

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

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) with c = 2.918012...

a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 9.

Mathematica

a = {}; r = 9; Do[AppendTo[a, r]; r = r^2 - r + 1, {n, 1, 10}]; a
NestList[#^2-#+1&, 9, 10] (* Harvey P. Dale, Aug 31 2014 *)

Crossrefs

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

Sequence in context: A367977 A197534 A015465 * A218872 A075232 A145524

Adjacent sequences: A144779 A144780 A144781 * A144783 A144784 A144785

Keyword

nonn

Author

Artur Jasinski, Sep 21 2008

Status

approved