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 1-3 of 3 results.

A147530 Numbers x such that there exists n in N : (x+1)^3 - x^3 = 103*n^2.

Original entry on oeis.org

51721, 6641322533431006, 852782015075257741682069713, 109501859241899449111168441436054160358, 14060635620199598267351285586436862449157290510201, 1805462258017787769335954916623470050495526664967434749114126
Offset: 1

Views

Author

Richard Choulet, Nov 06 2008

Keywords

Examples

			a(1)=51721 because the first relation is : 51722^3 - 51721^3 = 103*8827^2.

Links

Crossrefs

Cf. A147527, A147528, A147529.

Programs

  • GAP
    a:=[51721, 6641322533431006];; for n in [3..20] do a[n]:=128405450990*a[n-1] -a[n-2] +62402725494; od; a; # G. C. Greubel, Jan 12 2020
  • Magma
    I:=[51721, 6641322533431006]; [n le 2 select I[n] else 128405450990*Self(n-1) - Self(n-2) + 62402725494: n in [1..20]]; // G. C. Greubel, Jan 12 2020
  • Maple
    seq(coeff(series(x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x + x^2)), x, n+1), x, n), n = 1..20); # G. C. Greubel, Jan 12 2020
  • Mathematica
    LinearRecurrence[{128405450991,-128405450991,1}, {51721, 6641322533431006, 852782015075257741682069713}, 20] (* G. C. Greubel, Jan 12 2020 *)
  • PARI
    Vec(x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x+x^2)) + O(x^10)) \\ Colin Barker, Oct 21 2014, corrected Jul 13 2016
  • PARI
    isok(x) = issquare(((x+1)^3-x^3)/103) \\ Colin Barker, Jul 13 2016
  • Sage
    def A147530_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x + x^2)) ).list()
a=A147530_list(20); a[1:] # G. C. Greubel, Jan 12 2020

Formula

a(n+2) = 128405450990*a(n+1) - a(n) + 62402725494.
G.f.: x*(51721 + 64202725495*x - 51722*x^2)/((1-x)*(1 - 128405450990*x + x^2)). - Colin Barker, Oct 21 2014, corrected Jul 13 2016

Extensions

Editing and a(6) from Colin Barker, Oct 21 2014
a(3) to a(6) corrected by Colin Barker, Jul 13 2016

A147527 Numbers k such that there exists x in N : (x + 103)^3 - x^3 = k^2.

Original entry on oeis.org

93645643, 12024611022569890927, 1544025601332411913276450522087, 198261303679194296628699373223979621125203, 25457832112792289938442435570354101121237746019778883, 3268924413670798537740342016261657034171968745307560952072318967
Offset: 1

Views

Author

Richard Choulet, Nov 06 2008

Keywords

Examples

			a(1)=93645643 because the first relation is (5327263 + 103)^3 - 5327263^3 = 93645643^2.

Links

Crossrefs

Cf. A147528, A147529, A147530.

Programs

  • GAP
    a:=[93645643, 12024611022569890927];; for n in [3..20] do a[n]:=128405450990*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Jan 10 2020
  • Magma
    I:=[93645643, 12024611022569890927]; [n le 2 select I[n] else 128405450990*Self(n-1) - Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 10 2020
  • Maple
    seq(coeff(series(93645643*x*(1-x)/(1 - 128405450990*x + x^2), x, n+1), x, n), n = 0..20); # G. C. Greubel, Jan 10 2020
  • Mathematica
    LinearRecurrence[{128405450990,-1}, {93645643, 12024611022569890927}, 20] (* G. C. Greubel, Jan 10 2020 *)
  • PARI
    Vec(93645643*x*(1-x)/(1-128405450990*x+x^2) + O(x^20)) \\ Colin Barker, Oct 21 2014
  • Sage
    def A147527_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 93645643*x*(1-x)/(1 - 128405450990*x + x^2) ).list()
a=A147527_list(20); a[1:] # G. C. Greubel, Jan 10 2020

Formula

a(n+2) = 128405450990*a(n+1) - a(n).
G.f.: 93645643*x*(1-x)/(1 - 128405450990*x + x^2). - Colin Barker, Oct 21 2014
a(n) = sqrt((A147528(n) + 103)^3 - A147528(n)^3). - Michel Marcus, Jan 10 2020

Extensions

Editing and a(6) from Colin Barker, Oct 21 2014

A147529 Numbers n such that there exists x in N : (x+1)^3 - x^3 = 103*n^2.

Original entry on oeis.org

8827, 1133434915879903, 145539221541371657392445143, 18688029378753350610679552570834161667, 2399644840493193509137754319007833077692312755187, 308127477959355126566155341338642382333110448233345362623463
Offset: 1

Views

Author

Richard Choulet, Nov 06 2008

Keywords

Examples

			a(1)=8827 because the first relation is (51721+1)^3 - 51721^3 = 103*8827^2.

Links

Crossrefs

Cf. A147527, A147528, A147530.

Programs

  • GAP
    a:=[8827,1133434915879903];; for n in [3..20] do a[n]:=128405450990*a[n-1]+3*a[n-2]-a[n-3]; od; a; # G. C. Greubel, Jan 12 2020
  • Magma
    I:=[8827,1133434915879903]; [n le 2 select I[n] else 128405450990*Self(n-1) - Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 12 2020
  • Maple
    seq(coeff(series(8827*x*(1-x)/(1-128405450990*x+x^2), x, n+1), x, n), n = 1..20); # G. C. Greubel, Jan 12 2020
  • Mathematica
    LinearRecurrence[{128405450990,-1}, {8827,1133434915879903}, 20] (* G. C. Greubel, Jan 12 2020 *)
  • PARI
    Vec(8827*x*(1-x)/(1-128405450990*x+x^2) + O(x^20)) \\ Colin Barker, Oct 21 2014
  • Sage
    def A147529_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 8827*x*(1-x)/(1-128405450990*x+x^2) ).list()
a=A147529_list(20); a[1:] # G. C. Greubel, Jan 12 2020

Formula

a(n+2) = 128405450990*a(n+1) - a(n).
G.f.: 8827*x*(1-x) / (1 - 128405450990*x + x^2). - Colin Barker, Oct 21 2014

Extensions

Editing and a(6) from Colin Barker, Oct 21 2014
Showing 1-3 of 3 results.

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