A164135 Numbers k such that k^2 == 2 (mod 47).

7, 40, 54, 87, 101, 134, 148, 181, 195, 228, 242, 275, 289, 322, 336, 369, 383, 416, 430, 463, 477, 510, 524, 557, 571, 604, 618, 651, 665, 698, 712, 745, 759, 792, 806, 839, 853, 886, 900, 933, 947, 980, 994, 1027, 1041, 1074, 1088, 1121, 1135, 1168, 1182

Offset

1,1

Comments

Numbers congruent to {7, 40} mod 47. - Amiram Eldar, Feb 26 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

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

a(n) = (47+19*(-1)^n+94*(n-1))/4.

G.f.: x*(7+33*x+7*x^2)/((1+x)*(x-1)^2). - R. J. Mathar, Aug 26 2009

Sum_{n>=1} (-1)^(n+1)/a(n) = cot(7*Pi/47)*Pi/47. - Amiram Eldar, Feb 26 2023

Maple

A164135:=n->(47+19*(-1)^n+94*(n-1))/4: seq(A164135(n), n=1..100); # Wesley Ivan Hurt, Mar 30 2017

Mathematica

Select[Range[1200], Mod[#^2, 47] == 2 &] (* Vincenzo Librandi, Apr 06 2013 *)
Select[Range[2000], PowerMod[#, 2, 47]==2&] (* or *) LinearRecurrence[ {1, 1, -1}, {7, 40, 54}, 60] (* Harvey P. Dale, Sep 29 2013 *)

Prog

(Magma) [(47+19*(-1)^n+94*(n-1))/4: n in [1..60]]; // Vincenzo Librandi, Apr 06 2013

Crossrefs

Sequence in context: A203200 A165700 A249635 * A119056 A164083 A096200

Adjacent sequences: A164132 A164133 A164134 * A164136 A164137 A164138

Keyword

nonn,easy

Author

Vincenzo Librandi, Aug 11 2009

Extensions

Edited by R. J. Mathar, Aug 26 2009

Status

approved