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A176010
Positive numbers k such that k^2 == 2 (mod 97).
5
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
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: A199912 A082971 A374650 * A250562 A166819 A108683
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Apr 06 2010
STATUS
approved