OFFSET
0,2
COMMENTS
A variant of A000058, starting with an extra 1.
REFERENCES
Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année, MP, Dunod, 1997, Exercice 3.3.4 page 284.
LINKS
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.
Vjekoslav Kovač, On simultaneous rationality of two Ahmes series, arXiv:2406.17593 [math.NT], 2024.
FORMULA
For n>0, a(n) = A000058(n-1).
a(1) = 2, a(n+1) = a(n)^2 - a(n) + 1. a(n) = round(c^(2^n)), where c = 1.264... is the Vardi constant, A076393. - Thomas Ordowski, Jun 11 2013
From Bernard Schott, Apr 06 2021: (Start)
Sum_{n>=0} 1/a(n) = 2.
Sum_{n>=0} (-1)^(n+1)/a(n) = 2 * (A118227 - 1). (End)
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Product[a[k], {k, 0, n - 1}] + 1
PROG
(Haskell)
a129871 n = a129871_list !! n
a129871_list = 1 : a000058_list -- Reinhard Zumkeller, Dec 18 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Ben Branman, Sep 16 2011
EXTENSIONS
Corrected and rewritten by Ben Branman, Sep 16 2011
Edited by Max Alekseyev, Oct 11 2012
STATUS
approved