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

93645643, 12024611022569890927, 1544025601332411913276450522087, 198261303679194296628699373223979621125203, 25457832112792289938442435570354101121237746019778883, 3268924413670798537740342016261657034171968745307560952072318967

Offset: 1

Author

Richard Choulet, Nov 06 2008

Keywords

• easy
• nonn

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..50
• Index entries for linear recurrences with constant coefficients, signature (128405450990,-1).

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