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

1,3

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

Links

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

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)

Example

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

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 *)

Crossrefs

Sequence in context: A207968 A207671 A154328 * A362987 A235828 A102695

Adjacent sequences: A112651 A112652 A112653 * A112655 A112656 A112657

Keyword

nonn,easy

Author

Jeremy Gardiner, Dec 28 2005

Status

approved