A112651 Numbers k such that k^2 == k (mod 11).

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

Offset

1,3

Comments

Numbers that are congruent to {0,1} (mod 11). - Philippe Deléham, Oct 17 2011

Links

Table of n, a(n) for n=1..56.

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: A367340 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