A076393 -id:A076393 - cp's OEIS frontend

A144809 Decimal expansion of the constant 3.39277252592669675143137... arising in A144785.

3, 3, 9, 2, 7, 7, 2, 5, 2, 5, 9, 2, 6, 6, 9, 6, 7, 5, 1, 4, 3, 1, 3, 7, 0, 6, 5, 0, 1, 8, 1, 8, 7, 3, 7, 6, 8, 4, 7, 2, 0, 6, 6, 1, 5, 3, 0, 8, 5, 9, 8, 7, 8, 4, 6, 5, 4, 6, 0, 3, 6, 9, 2, 3, 1, 2, 1, 7, 2, 4, 7, 5, 9, 2, 4, 5, 9, 9, 0, 2, 6, 8, 3, 7, 9, 4, 0, 7, 5, 8, 0, 1, 3, 7, 5, 9, 3, 2, 4, 8, 8, 1, 4, 5, 5

Offset: 1

Artur Jasinski, Sep 21 2008

Cf. A076393, A144785, A144802, A144803, A144804, A144805, A144806, A144807, A144808, A144810, A144811, A144812.

A129871 A variant of Sylvester's sequence: a(0)=1 and for n>0, a(n) = (a(0)a(1)...*a(n-1)) + 1.

Original entry on oeis.org

1, 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, 12864938683278671740537145998360961546653259485195807

Offset: 0

Ben Branman, Sep 16 2011

nonn

A variant of A000058, starting with an extra 1.

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

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.
Junnosuke Koizumi, Irrationality of the reciprocal sum of doubly exponential sequences, arXiv:2504.05933 [math.NT], 2025.
Vjekoslav Kovač, On simultaneous rationality of two Ahmes series, arXiv:2406.17593 [math.NT], 2024.

Cf. A000058 which is the main entry for this sequence.

Cf. A118227.

a129871 n = a129871_list !! n
a129871_list = 1 : a000058_list  -- Reinhard Zumkeller, Dec 18 2013

a[0] = 1; a[n_] := a[n] = Product[a[k], {k, 0, n - 1}] + 1

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)

Corrected and rewritten by Ben Branman, Sep 16 2011

Edited by Max Alekseyev, Oct 11 2012

A077125 Decimal expansion of the constant c such that A007018(n)=floor(c^(2^n)).

Original entry on oeis.org

1, 5, 9, 7, 9, 1, 0, 2, 1, 8, 0, 3, 1, 8, 7, 3, 1, 7, 8, 3, 3, 8, 0, 7, 0, 1, 1, 8, 1, 5, 7, 4, 5, 5, 3, 1, 2, 3, 6, 2, 2, 2, 4, 9, 5, 3, 1, 8, 2, 1, 1, 4, 1, 9, 6, 5, 9, 1, 3, 9, 3, 0, 9, 4, 2, 2, 9, 6, 1, 6, 1, 9, 5, 6, 2, 2, 7, 9, 4, 9, 6, 8, 7, 6, 1, 1, 4, 7, 0, 6, 2, 8, 1, 9, 6, 3, 5, 1, 8, 2, 5, 0, 5, 6, 6

Offset: 1

Benoit Cloitre, Nov 29 2002

			1.5979102180318731783380....

Steven Finch, Exercises in Iterational Asymptotics, arXiv:2411.16062 [math.NT], 2024. See p. 9.
Nicolas Gast and Bruno Gaujal, Infinite labeled trees: from rational to Sturmian trees, Theor. Comput. Sci. 411 (2010) 1146-1166, Section 5.2.

Cf. A007018, A076393.

Equals lim_{n -> oo} A007018(n)^(1/2^n).

Equals E^2 where E is the Vardi constant arising in the Sylvester sequence (A076393). - Gerald McGarvey, Dec 08 2007

cp's OEIS Frontend

A144809 Decimal expansion of the constant 3.39277252592669675143137... arising in A144785.

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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.

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A077125 Decimal expansion of the constant c such that A007018(n)=floor(c^(2^n)).

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cp's OEIS Frontend

A144809 Decimal expansion of the constant 3.39277252592669675143137... arising in A144785.

Views

Author

Keywords

Crossrefs

A129871 A variant of Sylvester's sequence: a(0)=1 and for n>0, a(n) = (a(0)*a(1)*...*a(n-1)) + 1.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Haskell

Mathematica

Formula

Extensions

A077125 Decimal expansion of the constant c such that A007018(n)=floor(c^(2^n)).

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A129871 A variant of Sylvester's sequence: a(0)=1 and for n>0, a(n) = (a(0)a(1)...*a(n-1)) + 1.