This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A129871 #55 Apr 08 2025 23:29:33
%S A129871 1,2,3,7,43,1807,3263443,10650056950807,113423713055421844361000443,
%T A129871 12864938683278671740537145998360961546653259485195807
%N A129871 A variant of Sylvester's sequence: a(0)=1 and for n>0, a(n) = (a(0)*a(1)*...*a(n-1)) + 1.
%C A129871 A variant of A000058, starting with an extra 1.
%D A129871 Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année, MP, Dunod, 1997, Exercice 3.3.4 page 284.
%H A129871 Mohammad K. Azarian, <a href="http://www.jstor.org/stable/10.4169/college.math.j.42.4.329">Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958</a>, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330.
%H A129871 Mohammad K. Azarian, <a href="http://www.jstor.org/stable/10.4169/college.math.j.43.4.337">Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Solution</a> College Mathematics Journal, Vol. 43, No. 4, September 2012, pp. 340-342.
%H A129871 Junnosuke Koizumi, <a href="https://arxiv.org/abs/2504.05933">Irrationality of the reciprocal sum of doubly exponential sequences</a>, arXiv:2504.05933 [math.NT], 2025.
%H A129871 Vjekoslav Kovač, <a href="https://arxiv.org/abs/2406.17593">On simultaneous rationality of two Ahmes series</a>, arXiv:2406.17593 [math.NT], 2024.
%F A129871 For n>0, a(n) = A000058(n-1).
%F A129871 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
%F A129871 From _Bernard Schott_, Apr 06 2021: (Start)
%F A129871 Sum_{n>=0} 1/a(n) = 2.
%F A129871 Sum_{n>=0} (-1)^(n+1)/a(n) = 2 * (A118227 - 1). (End)
%t A129871 a[0] = 1; a[n_] := a[n] = Product[a[k], {k, 0, n - 1}] + 1
%o A129871 (Haskell)
%o A129871 a129871 n = a129871_list !! n
%o A129871 a129871_list = 1 : a000058_list -- _Reinhard Zumkeller_, Dec 18 2013
%Y A129871 Cf. A000058 which is the main entry for this sequence.
%Y A129871 Cf. A118227.
%K A129871 nonn
%O A129871 0,2
%A A129871 _Ben Branman_, Sep 16 2011
%E A129871 Corrected and rewritten by _Ben Branman_, Sep 16 2011
%E A129871 Edited by _Max Alekseyev_, Oct 11 2012