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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. - From 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

a(n) = 11*n/2-31/4-9*(-1)^n/4. G.f. x^2*(1+10*x) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

a(n+1)=Sum_k>=0 {A030308(n,k)*A005015(k-1)} with A005015(-1)=1. - From Philippe Deléham, Oct 17 2011.

EXAMPLE

12 is a member 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

Sequence in context: A084855 A101233 A118512 * A215027 A105945 A139114

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 January 21 19:40 EST 2019. Contains 319350 sequences. (Running on oeis4.)