A156840 Numbers k >= 1 such that k^2 == 1 (mod 900).

1, 199, 251, 449, 451, 649, 701, 899, 901, 1099, 1151, 1349, 1351, 1549, 1601, 1799, 1801, 1999, 2051, 2249, 2251, 2449, 2501, 2699, 2701, 2899, 2951, 3149, 3151, 3349, 3401, 3599, 3601, 3799, 3851, 4049, 4051, 4249, 4301, 4499, 4501, 4699, 4751, 4949, 4951

Offset

0,2

Comments

Numbers k such that k is +-1 mod 4, 9, and 25. - Charles R Greathouse IV, Dec 23 2011

Numbers congruent to {1, 199, 251, 449} mod 450. - Philippe Deléham, Dec 02 2016

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000 (corrected by Ray Chandler, Jan 19 2019)

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

a(n) = a(n-4) + 450.

a(n) = a(n-1) + a(n-4) - a(n-5). - R. J. Mathar, Aug 18 2009

From Jon E. Schoenfield, Jun 19 2010: (Start)

a(n) = (2*n + 1)*225/4 + f(n mod 4)/4, where f(0)=-221, f(1)=121, f(2)=-121, f(3)=221, so a nonrecursive formula for a(n) is

a(n) = (450*n + 225 - (100*floor(((n-1) mod 4)/2) + 121)*(-1)^n)/4. (End)

G.f.: x*(199 + 52*x + 198*x^2 + 2*x^3 - x^4)/((1 - x)^2*(1 + x)*(1 + x^2)). - Colin Barker, Apr 10 2012

Sum_{n>=0} (-1)^n/a(n) = (cot(Pi/450) - tan(13*Pi/225))*Pi/450. - Amiram Eldar, Feb 28 2023

Mathematica

LinearRecurrence[{1, 0, 0, 1, -1}, {199, 251, 449, 451, 649}, 50]  (* Harvey P. Dale, Apr 29 2011 *)
Select[Range[5000], PowerMod[#, 2, 900]==1&] (* Harvey P. Dale, May 05 2018 *)

Prog

(PARI) a(n)=n\8*900+[1, 199, 251, 449, 451, 649, 701, 899][n%8+1] \\ Charles R Greathouse IV, Dec 23 2011

Crossrefs

Sequence in context: A160342 A225575 A252667 * A227517 A142232 A166459

Adjacent sequences: A156837 A156838 A156839 * A156841 A156842 A156843

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 17 2009

Extensions

Edited and a(11) corrected by R. J. Mathar, Aug 18 2009

Status

approved