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

Author

Vincenzo Librandi, Jan 22 2009

Keywords

• nonn
• easy

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).

Programs

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 *)

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

Extensions

New name from Charles R Greathouse IV, Jan 11 2012