A144803 -id:A144803 - cp's OEIS frontend

A144779 Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 5.

5, 21, 421, 176821, 31265489221, 977530816197201697621, 955566496615167328821993756200407115362021, 913107329453384594090655605142589591944556891901674138343716072975722193082773842421

Offset: 1

Artur Jasinski, Sep 21 2008

nonn

			a(0) = 4, a(1) = 4+1 = 5, a(2) = 4*5+1 = 21, a(3) = 4*5*21+1 = 421, a(4) = 4*5*21*421+1 = 176821, ... - _Philippe Deléham_, Apr 19 2013

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, A144780, A144781, A144782, A144783, A144784, A144785, A144786, A144787, A144788.

a = {}; k = 5; Do[AppendTo[a, k]; k = k^2 - k + 1, {n,1,10}]; a (* Artur Jasinski, Sep 21 2008 *)
NestList[#^2-#+1&,5,8] (* Harvey P. Dale, Jan 17 2012 *)

a(n) = round(2.127995907464107054577351...)^(2^n) = round(A144803^(2^n)). [corrected by Joerg Arndt, Jan 15 2021]

a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 5.

A144808 Decimal expansion of the constant 3.242214032005686241449842754211782... arising in A144784.

Original entry on oeis.org

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

Offset: 1

Artur Jasinski, Sep 21 2008

Cf. A144784.

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

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

A144779 Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 5.

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A144808 Decimal expansion of the constant 3.242214032005686241449842754211782... arising in A144784.

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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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