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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. 5
 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 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 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 MATHEMATICA a = 1; a[n_] := a[n] = Product[a[k], {k, 1, 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. Sequence in context: A113845 A072713 A000058 * A075442 A082993 A071580 Adjacent sequences:  A129868 A129869 A129870 * A129872 A129873 A129874 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

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Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)