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A112654 Numbers n such that n^3 is congruent to n (mod 11). 2
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 (list; graph; refs; listen; history; text; internal format)
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)

Closed form: a(n) = 11/3*n + (8/9*i)*sqrt(3)*((-1/2+(1/2*i)*sqrt(3))^n - (-1/2-(1/2*i)*sqrt(3))^n), where i=sqrt(-1). - Paolo P. Lava, Apr 11 2012

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 * A235828 A102695 A252481

Adjacent sequences:  A112651 A112652 A112653 * A112655 A112656 A112657

KEYWORD

nonn,easy

AUTHOR

Jeremy Gardiner, Dec 28 2005

STATUS

approved

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Last modified July 22 20:51 EDT 2019. Contains 325226 sequences. (Running on oeis4.)