A112654 Numbers k such that k^3 == k (mod 11).

0, 1, 10, 11, 12, 21, 22, 23, 32, 33, 34, 43, 44, 45, 54, 55, 56, 65, 66, 67, 76, 77, 78, 87, 88, 89, 98, 99, 100, 109, 110, 111, 120, 121, 122, 131, 132, 133, 142, 143, 144, 153, 154, 155, 164, 165, 166, 175, 176, 177, 186, 187, 188, 197, 198, 199, 208, 209

Offset: 1

Author

Jeremy Gardiner, Dec 28 2005

Keywords

• nonn
• easy

Comments

Nonnegative integers m such that floor(k*m^2/11) = k*floor(m^2/11), where k can assume the values from 4 to 10. See the second comment in A265187. - Bruno Berselli, Dec 03 2015

Examples

			a(3) = 11 because 11^3 = 1331 == 0 (mod 11) and 11 == 0 (mod 11).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Maple

m = 11 for n = 1 to 300 if n^3 mod m = n mod m then print n; next n

Mathematica

Select[Range@ 209, Mod[#, 11] == Mod[#^3, 11] &] (* Michael De Vlieger, Dec 03 2015 *)
Select[Range[0,250],PowerMod[#,3,11]==Mod[#,11]&] (* Harvey P. Dale, May 15 2016 *)

Formula

From Colin Barker, Apr 11 2012: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4).

G.f.: x^2*(1+9*x+x^2)/((1-x)^2*(1+x+x^2)). (End)