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A155098
Numbers k such that k^2 == -1 (mod 41).
6
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
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
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 20 2009
EXTENSIONS
Terms checked & minor edits by M. F. Hasler, Jun 16 2010
STATUS
approved