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

Author

Vincenzo Librandi, Jan 20 2009

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

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 *)

PARI

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

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

Extensions

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