A241407 Numbers n such that n^2 == -1 (mod 73).

27, 46, 100, 119, 173, 192, 246, 265, 319, 338, 392, 411, 465, 484, 538, 557, 611, 630, 684, 703, 757, 776, 830, 849, 903, 922, 976, 995, 1049, 1068, 1122, 1141, 1195, 1214, 1268, 1287, 1341, 1360, 1414, 1433, 1487, 1506, 1560, 1579, 1633, 1652, 1706, 1725

Offset

1,1

Comments

Numbers n such that n == 27 or 46 (mod 73).

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*(27 + 19*x + 27*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) + 73 for all n>2.

a(n) = -27*(-1)^n + 73*floor(n/2).

Mathematica

Select[Range[1500], PowerMod[#, 2, 73] == 72 &] (* or *) CoefficientList[ Series[(27 + 19 x + 27 x^2)/((1 + x) (1 - x)^2), {x, 0, 100}], x]
Table[73n+{27, 46}, {n, 0, 30}]//Flatten (* or *) LinearRecurrence[{1, 1, -1}, {27, 46, 100}, 60] (* Harvey P. Dale, Jun 13 2017 *)

Prog

(Magma) I:=[27, 46, 100]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..50]] /* or */ [-27*(-1)^n+73*Floor(n/2): n in [1..50]];

Crossrefs

Cf. similar sequences listed in A155107.

Sequence in context: A275250 A223019 A059658 * A153260 A254209 A155137

Adjacent sequences: A241404 A241405 A241406 * A241408 A241409 A241410

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 25 2014

Status

approved