A155097 Numbers k such that k^2 == -1 (mod 37).

6, 31, 43, 68, 80, 105, 117, 142, 154, 179, 191, 216, 228, 253, 265, 290, 302, 327, 339, 364, 376, 401, 413, 438, 450, 475, 487, 512, 524, 549, 561, 586, 598, 623, 635, 660, 672, 697, 709, 734, 746, 771, 783, 808, 820, 845, 857, 882, 894, 919, 931, 956, 968

Offset

1,1

Comments

Numbers k such that k == 6 or 31 (mod 37). - 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) = 6*(-1)^(n+1) + 37*floor(n/2).

a(2k+1) = 37*k + a(1), a(2k) = 37*k - a(1), with a(1) = A002314(5) since 37 = A002144(5).

a(n) = a(n-2) + 37 for all n > 2. (End)

G.f.: x*(6 + 25*x + 6*x^2)/((1 + x)*(1 - x)^2). - Vincenzo Librandi, May 03 2014

Sum_{n>=1} (-1)^(n+1)/a(n) = cot(6*Pi/37)*Pi/37. - Amiram Eldar, Feb 26 2023

Mathematica

LinearRecurrence[{1, 1, -1}, {6, 31, 43}, 100] (* Vincenzo Librandi, Feb 29 2012 *)
Select[Range[1000], PowerMod[#, 2, 37]==36&] (* Harvey P. Dale, May 06 2012 *)
CoefficientList[Series[(6 + 25 x + 6 x^2)/((1 + x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, May 03 2014 *)

Prog

(PARI) A155097(n)=n\2*37-6*(-1)^n /* M. F. Hasler, Jun 16 2010 */

Crossrefs

Cf. A002144, A155086, A155095, A155096, A155098.

Sequence in context: A101340 A156825 A043058 * A306331 A254502 A025524

Adjacent sequences: A155094 A155095 A155096 * A155098 A155099 A155100

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 20 2009

Extensions

Terms checked, a(28) corrected, and minor edits by M. F. Hasler, Jun 16 2010

Status

approved