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 1-7 of 7 results.

A230151 Decimal expansion of the positive real solution of the equation x^4 + x^3 - 1 = 0.

Original entry on oeis.org

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

Views

Author

Paolo P. Lava, Oct 11 2013

Keywords

Comments

Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-3.

Examples

			0.8191725133961644396995711883424270403484978325537129656...

Links

Crossrefs

Cf. A086106 (other real root).
Cf. A075778, A230152-A230158.

Programs

  • Maple
    with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
print(evalf(a,1000)); end: P(1000,-3);
  • Mathematica
    Root[(#^4+#^3-1)&, 2] // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Feb 18 2014 *)
  • PARI
    polrootsreal(x^4+x^3-1)[2] \\ Charles R Greathouse IV, Feb 04 2025

A230152 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=4.

Original entry on oeis.org

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

Views

Author

Paolo P. Lava, Oct 11 2013

Keywords

Comments

Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-4.

Examples

			0.8566748838545028748523248153124343698313999454937526255...

Links

Crossrefs

Cf. A075778, A230151, A230153-A230158, A377080.

Programs

  • Maple
    with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
print(evalf(a,1000)); end: P(1000,-4);
  • Mathematica
    Root[x^5 + x^4 - 1, 1] // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Feb 18 2014 *)

A230154 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=6.

Original entry on oeis.org

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

Views

Author

Paolo P. Lava, Oct 11 2013

Keywords

Comments

Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-6.

Examples

			0.8986537126286992932608757220468058862604482200934396966...

Links

Crossrefs

Cf. A075778, A230151, A230152, A230153, A230155, A230156, A230157, A230158, A230160, A377081.

Programs

  • Maple
    with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
print(evalf(a,1000)); end: P(1000,-6);
  • Mathematica
    RealDigits[x/.FindRoot[x^7+x^6==1,{x,1},WorkingPrecision->120]][[1]] (* Harvey P. Dale, Dec 30 2013 *)

Formula

Equals 1/A230160. - Hugo Pfoertner, Oct 15 2024

A230156 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=8.

Original entry on oeis.org

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

Views

Author

Paolo P. Lava, Oct 11 2013

Keywords

Comments

Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-8.

Examples

			0.9215993196339830062994303152019693942536803842533707898...

Links

Crossrefs

Cf. A075778, A230151-A230155, A230157, A230158.

Programs

  • Maple
    with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
print(evalf(a,1000)); end: P(1000,-8);
  • Mathematica
    Root[x^9 + x^8 - 1, 1] // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Feb 18 2014 *)

A230157 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=9.

Original entry on oeis.org

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

Views

Author

Paolo P. Lava, Oct 11 2013

Keywords

Comments

Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-9.

Examples

			0.9295701282320228642044130369144641254353258530020248336...

Links

Crossrefs

Cf. A075778, A230151-A230156, A230158.

Programs

  • Maple
    with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
print(evalf(a,1000)); end: P(1000,-9);
  • Mathematica
    Root[x^10 + x^9 - 1, 2] // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Feb 18 2014 *)

A230153 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=5.

Original entry on oeis.org

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

Views

Author

Paolo P. Lava, Oct 11 2013

Keywords

Comments

Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-5.

Examples

			0.8812714616335695944076491628413720252791939793788952636...

Links

Crossrefs

Cf. A075778, A230151, A230152, A230154-A230158.

Programs

  • Maple
    with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
print(evalf(a,1000)); end: P(1000,-5);
  • Mathematica
    Root[x^6 + x^5 - 1, 2] // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Feb 18 2014 *)

A230155 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=7.

Original entry on oeis.org

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

Views

Author

Paolo P. Lava, Oct 11 2013

Keywords

Comments

Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-7.

Examples

			0.9115923534820549186286736724940501773758846943614139469...

Links

Crossrefs

Cf. A075778, A230151-A230154, A230156-A230158.

Programs

  • Maple
    with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
print(evalf(a,1000)); end: P(1000,-7);
  • Mathematica
    Root[x^8 + x^7 - 1, 2] // RealDigits[#, 10, 130]& // First (* Jean-François Alcover, Feb 18 2014 *)
Showing 1-7 of 7 results.

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