A155095 Numbers k such that k^2 == -1 (mod 17).

4, 13, 21, 30, 38, 47, 55, 64, 72, 81, 89, 98, 106, 115, 123, 132, 140, 149, 157, 166, 174, 183, 191, 200, 208, 217, 225, 234, 242, 251, 259, 268, 276, 285, 293, 302, 310, 319, 327, 336, 344, 353, 361, 370, 378, 387, 395, 404, 412, 421, 429, 438, 446, 455

Offset

1,1

Comments

The first pair (a,b) is such that a+b=p, a*b=p*h+1, with h<=(p-1)/4; other pairs are given by(a+kp, b+kp), k=1,2,3...

Numbers congruent to {4, 13} mod 17. - Amiram Eldar, Feb 27 2023

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) = 4*(-1)^(n+1) + 17*floor(n/2).

a(2k+1) = 17 k + a(1), a(2k) = 17 k - a(1), with a(1) = A002314(3) since 17 = A002144(3).

a(n) = a(n-2) + 17 for all n > 2. (End)

From Bruno Berselli, Sep 26 2010: (Start)

G.f.: x*(4+9*x+4*x^2)/((1+x)*(1-x)^2).

a(n) - a(n-1) - a(n-2) + a(n-3) = 0 for n > 3.

a(n) = (34*n + (-1)^n - 17)/4. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = tan(9*Pi/34)*Pi/17. - Amiram Eldar, Feb 27 2023

Mathematica

Select[Range[500], PowerMod[#, 2, 17]==16&] (* or *) LinearRecurrence[ {1, 1, -1}, {4, 13, 21}, 60] (* Harvey P. Dale, Jun 25 2011 *)

Prog

(PARI) A155095(n)=n\2*17-4*(-1)^n /* M. F. Hasler, Jun 16 2010 */

Crossrefs

Cf. A002144, A155086, A155096, A155097, A155098.

Sequence in context: A339271 A081024 A339216 * A063219 A063121 A199798

Adjacent sequences: A155092 A155093 A155094 * A155096 A155097 A155098

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 20 2009

Extensions

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

Status

approved