A144808 -id:A144808 - cp's OEIS frontend

A144784 Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 11.

11, 111, 12211, 149096311, 22229709804712411, 494159998001727075769152612720511, 244194103625066907517263589918036880566782292998362610615987380611

Offset: 1

Artur Jasinski, Sep 21 2008

nonn

For the "exact" formula, compare the Aho-Sloane reference in A000058. - N. J. A. Sloane, Apr 07 2014

A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)
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.

Cf. A000058, A082732, A144779, A144780, A144781, A144782, A144783, A144784, A144785, A144786, A144787, A144788, A144808.

See A239900 for another version.

a = {}; r = 11; Do[AppendTo[a, r]; r = r^2 - r + 1, {n, 1, 10}]; a

a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 11.

a(n) ~ c^(2^n) where c = 3.242214... (see A144808).

A144810 Decimal expansion of the constant c= 1.240554576397679299452... arising in A144787.

Original entry on oeis.org

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

Offset: 1

Artur Jasinski, Sep 22 2008

A076393, A144802, A144803, A144804, A144805, A144806, A144807, A144808, A144809, A144810, A144811, A144812

A144804 Decimal expansion of the constant 2.35011738402276... arising in A144780.

Original entry on oeis.org

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

Offset: 1

Artur Jasinski, Sep 21 2008

Cf. A144780.

Cf. A076393, A144802, A144803, A144805, A144806, A144807, A144808, A144809, A144810, A144811, A144812.

A144805 Decimal expansion of the constant 2.74167747444233776776... arising in A144781.

Original entry on oeis.org

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

Offset: 1

Artur Jasinski, Sep 21 2008

Cf. A076393, A144781, A144802, A144803, A144804, A144806, A144807, A144808, A144809, A144810, A144811, A144812.

A144807 Decimal expansion of the constant 3.0843510490691899023356932... arising in A144783.

Original entry on oeis.org

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

Offset: 1

Artur Jasinski, Sep 21 2008

Cf. A076393, A144783, A144802, A144803, A144804, A144805, A144806, A144808, A144809, A144810, A144811, A144812.

A144811 Decimal expansion of the constant c = 1.429887738657309204890861721408999... arising in A144788.

Original entry on oeis.org

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

Offset: 1

Artur Jasinski, Sep 22 2008

Cf. A076393, A144788, A144802, A144803, A144804, A144805, A144806, A144807, A144808, A144809, A144810, A144812.

c = 1.429887738657309204890861721408999...; A144788(n) = round(c^(3^n)).

A144802 Decimal expansion of the constant 1.880678543683078094492191765... arising in A082732.

Original entry on oeis.org

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

Offset: 1

Artur Jasinski, Sep 22 2008

Cf. A082732, A076393, A144803, A144804, A144805, A144806, A144807, A144808, A144809, A144810, A144811, A144812.

c=1.880678543683078094492191765...; A082732(n+2) = c^(2^n).

A144806 Decimal expansion of the constant 2.9180120691410773... arising in A144782.

Original entry on oeis.org

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

Offset: 1

Artur Jasinski, Sep 21 2008

Cf. A076393, A144782, A144802, A144803, A144804, A144805, A144807, A144808, A144809, A144810, A144811, A144812.

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

Original entry on oeis.org

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.

cp's OEIS Frontend

A144784 Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 11.

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A144810 Decimal expansion of the constant c= 1.240554576397679299452... arising in A144787.

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A144804 Decimal expansion of the constant 2.35011738402276... arising in A144780.

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A144805 Decimal expansion of the constant 2.74167747444233776776... arising in A144781.

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A144807 Decimal expansion of the constant 3.0843510490691899023356932... arising in A144783.

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A144811 Decimal expansion of the constant c = 1.429887738657309204890861721408999... arising in A144788.

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A144802 Decimal expansion of the constant 1.880678543683078094492191765... arising in A082732.

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A144806 Decimal expansion of the constant 2.9180120691410773... arising in A144782.

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

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