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

1,1

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.

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).

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 *)

Crossrefs

Cf. A000058, A082732, A144779, A144781, A144782, A144783, A144784, A144785, A144786, A144787, A144788, A144804.

Sequence in context: A120107 A015462 A006115 * A126976 A045159 A121002

Adjacent sequences: A144777 A144778 A144779 * A144781 A144782 A144783

Keyword

nonn,easy

Author

Artur Jasinski, Sep 21 2008

Extensions

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

Status

approved