login
A164135
Numbers k such that k^2 == 2 (mod 47).
5
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
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
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Aug 11 2009
EXTENSIONS
Edited by R. J. Mathar, Aug 26 2009
STATUS
approved