A176010 Positive numbers k such that k^2 == 2 (mod 97).

14, 83, 111, 180, 208, 277, 305, 374, 402, 471, 499, 568, 596, 665, 693, 762, 790, 859, 887, 956, 984, 1053, 1081, 1150, 1178, 1247, 1275, 1344, 1372, 1441, 1469, 1538, 1566, 1635, 1663, 1732, 1760, 1829, 1857, 1926, 1954, 2023, 2051, 2120, 2148, 2217

Offset

1,1

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

a(n) = (-97 + 41*(-1)^n + 194*n)/4.

a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3; a(1)=14, a(2)=83, a(3)=111.

a(n) = a(n-1) + 69 for n even, a(n) = a(n-1) + 28 for n odd, a(1)=14.

G.f.: x*(14+69*x+14*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Aug 24 2011

Sum_{n>=1} (-1)^(n+1)/a(n) = cot(14*Pi/97)*Pi/97. - Amiram Eldar, Feb 28 2023

Mathematica

Table[(97-41*(-1)^(n-1)+194*(n-1))/4, {n, 1, 50}] (* Vincenzo Librandi, Jul 13 2012 *)
Select[Range[2500], PowerMod[#, 2, 97]==2&] (* or *) LinearRecurrence[{1, 1, -1}, {14, 83, 111}, 50] (* Harvey P. Dale, Mar 28 2024 *)

Prog

(Magma) [(-97+41*(-1)^n+194*n)/4: n in [1..50]]; // Vincenzo Librandi, Jul 13 2012

Crossrefs

Sequence in context: A215700 A199912 A082971 * A250562 A166819 A108683

Adjacent sequences: A176007 A176008 A176009 * A176011 A176012 A176013

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 06 2010

Status

approved