A155450 Numbers congruent to 5 or 18 mod 23.

5, 18, 28, 41, 51, 64, 74, 87, 97, 110, 120, 133, 143, 156, 166, 179, 189, 202, 212, 225, 235, 248, 258, 271, 281, 294, 304, 317, 327, 340, 350, 363, 373, 386, 396, 409, 419, 432, 442, 455, 465, 478, 488, 501, 511, 524, 534, 547, 557, 570, 580, 593, 603, 616

Offset

1,1

Comments

Or, numbers n such that n^2 == 2 mod 23.

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

a(n) = a(n-1)+a(n-2)-a(n-3), with a(1)=5, a(2)=18, a(3)=28.

G.f.: x*(5 + 13*x + 5*x^2)/((1 + x)*(1 - x)^2). - Vincenzo Librandi, May 03 2014

Sum_{n>=1} (-1)^(n+1)/a(n) = cot(5*Pi/23)*Pi/23. - Amiram Eldar, Feb 26 2023

Mathematica

LinearRecurrence[{1, 1, -1}, {5, 18, 28}, 80] (* Vincenzo Librandi, Feb 29 2012 *)
CoefficientList[Series[(5 + 13 x + 5 x^2)/((1 + x) (1 - x)^2), {x, 0, 60}], x] (* Vincenzo Librandi, May 03 2014 *)

Crossrefs

Sequence in context: A055371 A034098 A034108 * A322409 A287894 A140365

Adjacent sequences: A155447 A155448 A155449 * A155451 A155452 A155453

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 22 2009

Extensions

New name from Charles R Greathouse IV, Jan 11 2012

Status

approved