A092464 Numbers congruent to 4 or 9 mod 13.

4, 9, 17, 22, 30, 35, 43, 48, 56, 61, 69, 74, 82, 87, 95, 100, 108, 113, 121, 126, 134, 139, 147, 152, 160, 165, 173, 178, 186, 191, 199, 204, 212, 217, 225, 230, 238, 243, 251, 256, 264, 269, 277, 282, 290, 295, 303, 308, 316, 321, 329, 334, 342, 347, 355, 360

Offset

1,1

Comments

Numbers k such that k^2 is congruent to 3 (modulo 13).

Links

Table of n, a(n) for n=1..56.

Index entries for linear recurrences with constant coefficients, signature (1, 1, -1).

Formula

From R. J. Mathar, Apr 20 2009: (Start)

a(n) = a(n-2) + 13 = a(n-1) + a(n-2) - a(n-3) = 13*n/2 - 13/4 - 3*(-1)^n/4.

G.f.: x*(4+5*x+4*x^2)/((1+x)*(x-1)^2). (End)

a(n) = 13*(n-1) - a(n-1), (with a(1)=4). - Vincenzo Librandi, Nov 17 2010

Sum_{n>=1} (-1)^(n+1)/a(n) = tan(5*Pi/26)*Pi/13. - Amiram Eldar, Feb 27 2023

Mathematica

Select[Range[400], MemberQ[{4, 9}, Mod[#, 13]]&] (* or *) Select[Range[400], PowerMod[#, 2, 13]==3&] (* Harvey P. Dale, Mar 05 2012 *)

Crossrefs

A127547 is a subsequence.

Sequence in context: A313355 A313356 A295494 * A328271 A354414 A173562

Adjacent sequences: A092461 A092462 A092463 * A092465 A092466 A092467

Keyword

nonn

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Mar 25 2004

Extensions

More terms from Ray Chandler, Mar 27 2004

Edited by N. J. A. Sloane, May 10 2007

Incorrect formula deleted by N. J. A. Sloane, Jun 16 2010

Status

approved