A155098 Numbers k such that k^2 == -1 (mod 41).

9, 32, 50, 73, 91, 114, 132, 155, 173, 196, 214, 237, 255, 278, 296, 319, 337, 360, 378, 401, 419, 442, 460, 483, 501, 524, 542, 565, 583, 606, 624, 647, 665, 688, 706, 729, 747, 770, 788, 811, 829, 852, 870, 893, 911, 934, 952, 975, 993, 1016, 1034, 1057

Offset

1,1

Comments

Numbers k such that k == 9 or 32 (mod 41). - Charles R Greathouse IV, Dec 27 2011

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

From M. F. Hasler, Jun 16 2010: (Start)

a(n) = 9*(-1)^(n+1) + 41*floor(n/2).

a(2k+1) = 41*k + a(1), a(2k) = 41*k - a(1), with a(1) = A002314(6) since 41 = A002144(6).

a(n) = a(n-2) + 41 for all n > 2. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = cot(9*Pi/41)*Pi/41. - Amiram Eldar, Feb 26 2023

Mathematica

LinearRecurrence[{1, 1, -1}, {9, 32, 50}, 100] (* Vincenzo Librandi, Feb 29 2012 *)
Select[Range[1100], PowerMod[#, 2, 41] == 40 &] (* Vincenzo Librandi, Apr 24 2014 *)

Prog

(PARI) A155098(n)=n\2*41-9*(-1)^n /* M. F. Hasler, Jun 16 2010 */

Crossrefs

Cf. A002144, A155086, A155095, A155096, A155097.

Sequence in context: A018833 A130510 A120498 * A063134 A027620 A152619

Adjacent sequences: A155095 A155096 A155097 * A155099 A155100 A155101

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 20 2009

Extensions

Terms checked & minor edits by M. F. Hasler, Jun 16 2010

Status

approved