A144779 Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 5.

5, 21, 421, 176821, 31265489221, 977530816197201697621, 955566496615167328821993756200407115362021, 913107329453384594090655605142589591944556891901674138343716072975722193082773842421

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) = round(2.127995907464107054577351...)^(2^n) = round(A144803^(2^n)). [corrected by Joerg Arndt, Jan 15 2021]

a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 5.

Example

a(0) = 4, a(1) = 4+1 = 5, a(2) = 4*5+1 = 21, a(3) = 4*5*21+1 = 421, a(4) = 4*5*21*421+1 = 176821, ... - Philippe Deléham, Apr 19 2013

Mathematica

a = {}; k = 5; Do[AppendTo[a, k]; k = k^2 - k + 1, {n, 1, 10}]; a (* Artur Jasinski, Sep 21 2008 *)
NestList[#^2-#+1&, 5, 8] (* Harvey P. Dale, Jan 17 2012 *)

Crossrefs

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

Sequence in context: A009732 A009758 A143503 * A193324 A220002 A156860

Adjacent sequences: A144776 A144777 A144778 * A144780 A144781 A144782

Keyword

nonn

Author

Artur Jasinski, Sep 21 2008

Status

approved