

A129871


A variant of Sylvester's sequence: a(0)=1 and for n>0, a(n) = (a(0)*a(1)*...*a(n1)) + 1.


7




OFFSET

0,2


COMMENTS

A variant of A000058, starting with an extra 1.


REFERENCES

JeanMarie Monier, Analyse, Exercices corrigés, 2ème année, MP, Dunod, 1997, Exercice 3.3.4 page 284.


LINKS

Table of n, a(n) for n=0..9.
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. 340342.


FORMULA

For n>0, a(n) = A000058(n1).
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

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



