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A155086
Numbers k such that k^2 == -1 (mod 13).
6
5, 8, 18, 21, 31, 34, 44, 47, 57, 60, 70, 73, 83, 86, 96, 99, 109, 112, 122, 125, 135, 138, 148, 151, 161, 164, 174, 177, 187, 190, 200, 203, 213, 216, 226, 229, 239, 242, 252, 255, 265, 268, 278, 281, 291, 294, 304, 307, 317, 320, 330, 333, 343, 346, 356, 359
OFFSET
1,1
COMMENTS
Numbers k such that k == 5 or 8 mod 13. - Charles R Greathouse IV, Dec 28 2011
FORMULA
a(n) = a(n-1)+a(n-2)-a(n-3).
G.f.: x*(5+3*x+5*x^2)/((1+x)*(x-1)^2) .
a(n) = 13*(n-1/2)/2 -7*(-1)^n/4.
a(n) = a(n-2)+13. - M. F. Hasler, Jun 16 2010
Sum_{n>=1} (-1)^(n+1)/a(n) = tan(3*Pi/26)*Pi/13. - Amiram Eldar, Feb 27 2023
MATHEMATICA
LinearRecurrence[{1, 1, -1}, {5, 8, 18}, 50] (* Vincenzo Librandi, Feb 26 2012 *)
Select[Range[1000], PowerMod[#, 2, 13] == 12 &] (* Vincenzo Librandi, Apr 24 2014 *)
PROG
(Magma) I:=[5, 8, 18]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 26 2012
CROSSREFS
Cf. A002144, A047221 (m=5), A155095 (m=17), A156619 (m=25), A155096 (m=29), A155097 (m=37), A155098 (m=41), A154609 (bisection).
Sequence in context: A359949 A291752 A237276 * A219049 A245534 A302393
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 20 2009
EXTENSIONS
Algebra simplified by R. J. Mathar, Aug 18 2009
Edited by N. J. A. Sloane, Jun 23 2010
STATUS
approved