A241520 Numbers k such that k^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

Author

Vincenzo Librandi, Apr 25 2014

Keywords

• nonn
• easy

Comments

Numbers k such that k == 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).

Crossrefs

Cf. similar sequences listed in A155107.

Programs

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]];

Magma

[-34*(-1)^n+89*Floor(n/2): n in [1..50]];

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]

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).