A241520 Numbers n such that n^2 == -1 (mod 89).

34, 55, 123, 144, 212, 233, 301, 322, 390, 411, 479, 500, 568, 589, 657, 678, 746, 767, 835, 856, 924, 945, 1013, 1034, 1102, 1123, 1191, 1212, 1280, 1301, 1369, 1390, 1458, 1479, 1547, 1568, 1636, 1657, 1725, 1746, 1814, 1835, 1903, 1924, 1992, 2013, 2081

Offset

1,1

Comments

Numbers n such that n == 34 or 55 mod 89.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x*(34 + 21*x + 34*x^2)/((1 + x)*(1 - x)^2).

a(n) = a(n-1) + a(n-2) - a(n-3) for n>2.

a(n) = a(n-2) + 89 for all n>2.

a(n) = -34*(-1)^n + 89*floor(n/2).

Mathematica

Select[Range[1500], PowerMod[#, 2, 89] == 88 &] (* or *) CoefficientList[Series[(34 + 21 x + 34 x^2)/((1 + x) (1 -x)^2), {x, 0, 100}], x]

Prog

(Magma) I:=[34, 55, 123]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..50]] /* or */ [-34*(-1)^n+89*Floor(n/2): n in [1..50]];

Crossrefs

Cf. similar sequences listed in A155107.

Sequence in context: A274380 A305061 A051969 * A067243 A171668 A259676

Adjacent sequences: A241517 A241518 A241519 * A241521 A241522 A241523

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 25 2014

Status

approved