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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 11 00:22 EST 2023. Contains 367717 sequences. (Running on oeis4.)