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

Author

Vincenzo Librandi, Aug 11 2009

Keywords

• nonn
• easy

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).

Programs

Magma

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

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 *)

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

Extensions

Edited by R. J. Mathar, Aug 26 2009