A155107 -id:A155107 - cp's OEIS frontend

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

Vincenzo Librandi, Apr 25 2014

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. similar sequences listed in A155107.

I:=[11,50,72]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..50]];

[-11*(-1)^n+61*Floor(n/2): n in [1..50]];

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]

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).

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

Original entry on oeis.org

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

Vincenzo Librandi, Apr 25 2014

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. similar sequences listed in A155107.

I:=[27,46,100]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..50]];

[-27*(-1)^n+73*Floor(n/2): n in [1..50]];

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 *)

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).

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

Original entry on oeis.org

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

Vincenzo Librandi, Apr 25 2014

Numbers k such that k == 34 or 55 (mod 89).

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. similar sequences listed in A155107.

I:=[34,55,123]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..50]];

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

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]

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).

A241521 Numbers k such that k^2 == -1 (mod 97).

Original entry on oeis.org

22, 75, 119, 172, 216, 269, 313, 366, 410, 463, 507, 560, 604, 657, 701, 754, 798, 851, 895, 948, 992, 1045, 1089, 1142, 1186, 1239, 1283, 1336, 1380, 1433, 1477, 1530, 1574, 1627, 1671, 1724, 1768, 1821, 1865, 1918, 1962, 2015, 2059, 2112, 2156, 2209, 2253

Offset: 1

Vincenzo Librandi, Apr 25 2014

Numbers k such that k == 22 or 75 (mod 97).

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. similar sequences listed in A155107.

I:=[22,75,119]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..50]];

[-22*(-1)^n+97*Floor(n/2): n in [1..50]];

Select[Range[1800], PowerMod[#, 2, 97] == 96 &] (* or *) CoefficientList[Series[(22 + 53 x + 22 x^2)/((1 + x) (1 - x)^2), {x, 0, 100}], x]

G.f.: x*(22 + 53*x + 22*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) + 97 for all n>2.
a(n) = -22*(-1)^n + 97*floor(n/2).

cp's OEIS Frontend

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

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

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

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A241521 Numbers k such that k^2 == -1 (mod 97).

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