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 A129871 A variant of Sylvester's sequence: a(0)=1 and for n>0, a(n) = (a(0)*a(1)*...*a(n-1)) + 1. 7
 1, 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, 12864938683278671740537145998360961546653259485195807 (list; graph; refs; listen; history; text; internal format)
 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. 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 = 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 Cf. A000058 which is the main entry for this sequence. Cf. A118227. Sequence in context: A113845 A072713 A000058 * A075442 A082993 A071580 Adjacent sequences:  A129868 A129869 A129870 * A129872 A129873 A129874 KEYWORD nonn,changed 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

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Last modified April 21 17:36 EDT 2021. Contains 343156 sequences. (Running on oeis4.)