A241406 Numbers n such that n^2 == -1 (mod 61).

11, 50, 72, 111, 133, 172, 194, 233, 255, 294, 316, 355, 377, 416, 438, 477, 499, 538, 560, 599, 621, 660, 682, 721, 743, 782, 804, 843, 865, 904, 926, 965, 987, 1026, 1048, 1087, 1109, 1148, 1170, 1209, 1231, 1270, 1292, 1331, 1353, 1392, 1414, 1453, 1475, 1514

Offset

1,1

Comments

Numbers n such that n == 11 or 50 (mod 61).

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*(11 + 39*x + 11*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) + 61 for all n>2.

a(n) = -11*(-1)^n + 61*floor(n/2).

Mathematica

Select[Range[1500], PowerMod[#, 2, 61] == 60 &] (* or *) CoefficientList[Series[(11 + 39 x + 11 x^2)/((1 + x) (1 - x)^2), {x, 0, 100}], x]

Prog

(Magma) I:=[11, 50, 72]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..50]] /* or */ [-11*(-1)^n+61*Floor(n/2): n in [1..50]];

Crossrefs

Cf. similar sequences listed in A155107.

Sequence in context: A284857 A241964 A306425 * A215728 A185019 A212560

Adjacent sequences: A241403 A241404 A241405 * A241407 A241408 A241409

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 25 2014

Status

approved