A147526 Numbers Y such that 309*Y^2 + 103 is a square.

103443, 13282645066862013, 1705564030150515483364139427, 219003718483798898222336882872108320717, 28121271240399196534702571172873724898314581020403, 3610924516035575538671909833246940100991053329934869498228253

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..90

Index entries for linear recurrences with constant coefficients, signature (128405450990,-1).

Formula

a(n) = sqrt((A147525(n)^2 - 103)/309). - Colin Barker, Oct 22 2014

G.f.: 103443*x*(1+x)/(1 - 128405450990*x + x^2). - Colin Barker, Oct 21 2014

Example

a(1)=103443 because the first relation is : 1818362^2=309*103443^2+103.

Maple

seq(coeff(series(103443*x*(1+x)/(1-128405450990*x+x^2), x, n+1), x, n), n = 1..20); # G. C. Greubel, Jan 10 2020

Mathematica

CoefficientList[Series[103443(1+x)/(1-128405450990x+x^2), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 22 2014 *)
LinearRecurrence[{128405450990, -1}, {103443, 13282645066862013}, 10] (* Harvey P. Dale, Sep 19 2020 *)

Prog

(PARI) Vec(103443*x*(1+x)/(1-128405450990*x+x^2) + O(x^20)) \\ Colin Barker, Oct 21 2014
(Magma) I:=[103443, 13282645066862013]; [n le 2 select I[n] else 128405450990*Self(n-1)-Self(n-2): n in [1..10]]; // Vincenzo Librandi, Oct 22 2014
(Sage)
def A147526_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 103443*x*(1+x)/(1-128405450990*x+x^2) ).list()
a=A147526_list(20); a[1:] # G. C. Greubel, Jan 10 2020
(GAP) a:=[103443, 13282645066862013];; for n in [3..20] do a[n]:=128405450990*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Jan 10 2020

Crossrefs

Cf. A147525.

Sequence in context: A250941 A237572 A255210 * A269218 A237894 A171162

Adjacent sequences: A147523 A147524 A147525 * A147527 A147528 A147529

Keyword

nonn,easy

Author

Richard Choulet, Nov 06 2008

Extensions

Errors in terms corrected, and a(6) added by Colin Barker, Oct 21 2014

Status

approved