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 A112651 Numbers n such that n^2 (mod 11) is congruent to n (mod 11). 4
 0, 1, 11, 12, 22, 23, 33, 34, 44, 45, 55, 56, 66, 67, 77, 78, 88, 89, 99, 100, 110, 111, 121, 122, 132, 133, 143, 144, 154, 155, 165, 166, 176, 177, 187, 188, 198, 199, 209, 210, 220, 221, 231, 232, 242, 243, 253, 254, 264, 265, 275, 276, 286, 287, 297, 298 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Numbers that are congruent to {0,1} mod 11. - Philippe Deléham, Oct 17 2011 LINKS Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA a(n) = 11*n - a(n-1) - 21 (with a(1)=0). - Vincenzo Librandi, Nov 13 2010 From R. J. Mathar, Oct 08 2011: (Start) a(n) = 11*n/2 - 31/4 - 9*(-1)^n/4. G.f.: x^2*(1+10*x) / ( (1+x)*(x-1)^2 ). (End) a(n+1) = Sum_{k>=0} A030308(n,k)*A005015(k-1) with A005015(-1)=1. - Philippe Deléham, Oct 17 2011 EXAMPLE 12 is a term because 12*12 = 144 = 1 (mod 11) and 12 = 1 (mod 11). MAPLE m = 11 for n = 1 to 300 if n^2 mod m = n mod m then print n; next n MATHEMATICA Select[Range[0, 300], PowerMod[#, 2, 11]==Mod[#, 11]&] (* or *) LinearRecurrence[ {1, 1, -1}, {0, 1, 11}, 60] (* Harvey P. Dale, Apr 19 2015 *) PROG (PARI) a(n)=11*n/2-31/4-9*(-1)^n/4 \\ Charles R Greathouse IV, Oct 16 2015 CROSSREFS Cf. A010880 (n mod 11), A070434 (n^2 mod 11). Cf. A005015, A030308. Sequence in context: A084855 A101233 A118512 * A215027 A331194 A105945 Adjacent sequences:  A112648 A112649 A112650 * A112652 A112653 A112654 KEYWORD easy,nonn AUTHOR Jeremy Gardiner, Dec 28 2005 EXTENSIONS Edited by N. J. A. Sloane, Aug 19 2010 Definition clarified by Harvey P. Dale, Apr 19 2015 STATUS approved

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Last modified December 1 16:17 EST 2020. Contains 338844 sequences. (Running on oeis4.)