A144783 - OEIS

A144783

Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 10.

10, 91, 8191, 67084291, 4500302031888391, 20252718378218776104731448680491, 410172601707440572557971589875869064610540321970215293555320591, 168241563191450680898537024308131628447885486994777537422995633998657738457104605412468520116391629012196009150161991233268691

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

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. Solution published in Vol. 43, No. 4, September 2012, pp. 340-342

LINKS

Table of n, a(n) for n=1..8.

FORMULA

a(n) = round((3.08435104906918990233569320020272148875011089837398848476442237096569...)^(2^n)) = round(A144807^(2^n)). [corrected by Joerg Arndt, Jan 15 2021]

a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 10.

MATHEMATICA

a = {}; r = 10; Do[AppendTo[a, r]; r = r^2 - r + 1, {n, 1, 10}]; a (* or *)

Table[Round[3.08435104906918990233569320020272148875011089837398848476442237096569188195734783139337492942278549518507672786196650938869338548385641623^(2^n)], {n, 1, 8}] (* Artur Jasinski *)

NestList[#^2-#+1&, 10, 8] (* Harvey P. Dale, May 07 2017 *)

CROSSREFS

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

Sequence in context: A267833 A354380 A015467 * A365217 A227512 A227513

Adjacent sequences: A144780 A144781 A144782 * A144784 A144785 A144786

KEYWORD

nonn

AUTHOR

Artur Jasinski, Sep 21 2008

STATUS

approved