cp's OEIS Frontend

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.

Showing 1-9 of 9 results.

A144783 Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 10.

Original entry on oeis.org

10, 91, 8191, 67084291, 4500302031888391, 20252718378218776104731448680491, 410172601707440572557971589875869064610540321970215293555320591, 168241563191450680898537024308131628447885486994777537422995633998657738457104605412468520116391629012196009150161991233268691
Offset: 1

Views

Author

Artur Jasinski, Sep 21 2008

Keywords

References

  • 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. Solution published in Vol. 43, No. 4, September 2012, pp. 340-342

Crossrefs

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

Programs

  • Mathematica
    a = {}; r = 10; Do[AppendTo[a, r]; r = r^2 - r + 1, {n, 1, 10}]; a (* or *)
Table[Round[3.08435104906918990233569320020272148875011089837398848476442237096569188195734783139337492942278549518507672786196650938869338548385641623^(2^n)], {n, 1, 8}] (* Artur Jasinski *)
NestList[#^2-#+1&,10,8] (* Harvey P. Dale, May 07 2017 *)

Formula

a(n) = round((3.08435104906918990233569320020272148875011089837398848476442237096569...)^(2^n)) = round(A144807^(2^n)). [corrected by Joerg Arndt, Jan 15 2021]
a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 10.

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

Views

Author

Artur Jasinski, Sep 21 2008

Keywords

Crossrefs

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

Views

Author

Artur Jasinski, Sep 22 2008

Keywords

Crossrefs

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

Views

Author

Artur Jasinski, Sep 21 2008

Keywords

Crossrefs

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

Views

Author

Artur Jasinski, Sep 21 2008

Keywords

Crossrefs

Cf. A076393, A144781, A144802, A144803, A144804, A144806, A144807, 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

Views

Author

Artur Jasinski, Sep 22 2008

Keywords

Crossrefs

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

Formula

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

Views

Author

Artur Jasinski, Sep 22 2008

Keywords

Crossrefs

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

Formula

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

Views

Author

Artur Jasinski, Sep 21 2008

Keywords

Crossrefs

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

Views

Author

Artur Jasinski, Sep 21 2008

Keywords

Crossrefs

Cf. A076393, A144785, A144802, A144803, A144804, A144805, A144806, A144807, A144808, A144810, A144811, A144812.
Showing 1-9 of 9 results.

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