A144780 Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 6.

6, 31, 931, 865831, 749662454731, 561993796032558961827631, 315837026779085485103718410756049100028793244531

Offset: 1

Author

Artur Jasinski, Sep 21 2008

Keywords

• nonn
• easy

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..11
• 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, A144779, A144781, A144782, A144783, A144784, A144785, A144786, A144787, A144788, A144804.

Programs

Mathematica

a = {}; k = 6; Do[AppendTo[a, k]; k = k^2 - k + 1, {n, 1, 10}]; a
NestList[#^2-#+1&,6,10] (* Harvey P. Dale, Dec 19 2024 *)

Formula

a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 6.

a(n) ~ c^(2^n) where is c is 2.350117384... (A144804).

Extensions

a(8) moved to b-file by Hugo Pfoertner, Aug 30 2020