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A241406 Numbers n such that n^2 == -1 (mod 61). 2
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 (list; graph; refs; listen; history; text; internal format)
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: A159486 A284857 A241964 * A215728 A185019 A212560

Adjacent sequences:  A241403 A241404 A241405 * A241407 A241408 A241409

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Apr 25 2014

STATUS

approved

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Last modified February 16 08:26 EST 2019. Contains 320159 sequences. (Running on oeis4.)