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 1-5 of 5 results.

A144743 Recurrence sequence a(n)=a(n-1)^2-a(n-1)-1, a(0)=3.

Original entry on oeis.org

3, 5, 19, 341, 115939, 13441735781, 180680260792773944179, 32645356640144805339284259388335434039861, 1065719310162246533488642668727242229836148490441005113524301742665845135502859459
Offset: 0

Views

Author

Artur Jasinski, Sep 20 2008

Keywords

Comments

a(0)=3 is the smallest integer generating an increasing sequence of the form a(n)=a(n-1)^2-a(n-1)-1.
Conjecture: A130282 and this sequence are disjoint. If this is true, for n >= 1, a(n+1) is the smallest m such that (m^2-1) / (a(n)^2-1) + 1 is a square. - Jianing Song, Mar 19 2022

Crossrefs

Cf. A000058, A082732, A144744, A144745, A144746, A144747, A144748.

Programs

  • Mathematica
    a = {3}; k = 3; Do[k = k^2 - k - 1; AppendTo[a, k], {n, 1, 10}]; a
  • PARI
    a(n,s=3)=for(i=1,n,s=s^2-s-1);s \\ M. F. Hasler, Oct 06 2014

Formula

a(n) = a(n-1)^2-a(n-1)-1, a(0)=3.
a(n) ~ c^(2^n), where c = 2.07259396780115004655284076205241023281287049774423620992171834046728756... . - Vaclav Kotesovec, May 06 2015

Extensions

Edited by M. F. Hasler, Oct 06 2014

A144744 Recurrence sequence a(n)=a(n-1)^2-a(n-1)-1, a(0)=4.

Original entry on oeis.org

4, 11, 109, 11771, 138544669, 19194625169774891, 368433635408155743950638444286989, 135743343700069833946317076518699443524748244656296738254150399131
Offset: 0

Views

Author

Artur Jasinski, Sep 20 2008

Keywords

Comments

a(0)=3 is the smallest integer generating an increasing sequence of the form a(n)=a(n-1)^2-a(n-1)-1.

Crossrefs

Cf. A000058, A082732, A144743, A144745, A144746, A144747, A144748.

Programs

  • Mathematica
    a = {}; k = 4; Do[k = k^2 - k - 1; AppendTo[a, k], {n, 1, 10}]; a
  • PARI
    a(n, s=4)={for(i=1, n, s=s^2-s-1); s} \\ M. F. Hasler, Oct 06 2014

Formula

a(n)=a(n-1)^2-a(n-1)-1 and a(0)=4.
a(n) ~ c^(2^n), where c = 3.22737450272053234771396610986262048906046050824600724014923334412606964... . - Vaclav Kotesovec, May 06 2015

Extensions

Edited by M. F. Hasler, Oct 06 2014

A144745 Recurrence sequence a(n)=a(n-1)^2-a(n-1)-1, a(0)=9.

Original entry on oeis.org

9, 71, 4969, 24685991, 609398126966089, 371366077149776919833628989831, 137912763257614063309949706968500684963726537144819872418729
Offset: 0

Views

Author

Artur Jasinski, Sep 20 2008

Keywords

Comments

The original version of this sequence had a(0)=5=A144743(1) and therefore was essentially the same as that sequence A144743.
The next term a(8) has 119 digits.

Crossrefs

Cf. A000058, A082732, A144743, A144744, A144746, A144747, A144748.

Programs

  • Mathematica
    k = 9; a = {k}; Do[k = k^2 - k - 1; AppendTo[a, k], {n, 1, 10}]; a
NestList[#^2 - # - 1 &, 9, 7]  (* Harvey P. Dale, Feb 04 2011 *)
  • PARI
    a(n,s=9)=for(i=1,n,s=s^2-s-1);s \\ M. F. Hasler, Oct 06 2014

Formula

a(n) = a(n-1)^2-a(n-1)-1 and a(0)=9.
a(n) ~ c^(2^n), where c = 8.395688554881795978328174160925857176207363473280394010762212170489... . - Vaclav Kotesovec, May 06 2015

Extensions

New initial value a(0)=9 from M. F. Hasler, Oct 20 2014

A144746 a(n) = a(n-1)^2 - a(n-1) - 1, a(0)=6.

Original entry on oeis.org

6, 29, 811, 656909, 431528777371, 186217085698878552894269, 34676803006183479266409218250231853558140150091, 1202480666729655584789949373132702064208272454072740050128160074167965751208292536045867158189
Offset: 0

Views

Author

Artur Jasinski, Sep 20 2008

Keywords

Comments

a(0)=3 is the smallest integer generating an increasing sequence of the form a(n) = a(n-1)^2 - a(n-1) - 1, cf. A144743.

Crossrefs

Cf. A000058, A082732, A144743, A144744, A144745, A144747, A144748.

Programs

  • Mathematica
    NestList[#^2-#-1&,6,8]  (* Harvey P. Dale, Jan 22 2011 *)
  • PARI
    a(n, s=6)={for(i=1, n, s=s^2-s-1);s} \\ M. F. Hasler, Oct 06 2014

Formula

a(n) = a(n-1)^2 - a(n-1) - 1 and a(0)=6.
a(n) ~ c^(2^n), where c = 5.33565954034691307256446890777476398311129407641143635105306409567572... . - Vaclav Kotesovec, May 06 2015

Extensions

Corrected and edited by M. F. Hasler, Oct 06 2014

A144747 Recurrence sequence a(n)=a(n-1)^2-a(n-1)-1, a(0)=7.

Original entry on oeis.org

7, 41, 1639, 2684681, 7207509387079, 51948191564824694742765161, 2698614606855723567054656642857156538246857652590759, 7282520796335071470236496456671241855257664867148949932302276253455702665493855273950765616767079605321
Offset: 0

Views

Author

Artur Jasinski, Sep 20 2008

Keywords

Comments

a(0)=3 is the smallest integer generating an increasing sequence of the form a(n)=a(n-1)^2-a(n-1)-1, cf. A144743.

Crossrefs

Cf. A000058, A082732, A144743, A144744, A144745, A144746, A144748.

Programs

  • Mathematica
    a = {}; k = 7; Do[k = k^2 - k - 1; AppendTo[a, k], {n, 1, 10}]; a
  • PARI
    a(n, s=7)={for(i=1, n, s=s^2-s-1);s} \\ M. F. Hasler, Oct 06 2014

Formula

a(n)=a(n-1)^2-a(n-1)-1 and a(0)=7.
a(n) ~ c^(2^n), where c = 6.3622623884585267364822329679498420997632627444610172910703030892754... . - Vaclav Kotesovec, May 06 2015

Extensions

Edited by M. F. Hasler, Oct 06 2014
Showing 1-5 of 5 results.

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