A036117 a(n) = 2^n mod 11.

1, 2, 4, 8, 5, 10, 9, 7, 3, 6, 1, 2, 4, 8, 5, 10, 9, 7, 3, 6, 1, 2, 4, 8, 5, 10, 9, 7, 3, 6, 1, 2, 4, 8, 5, 10, 9, 7, 3, 6, 1, 2, 4, 8, 5, 10, 9, 7, 3, 6, 1, 2, 4, 8, 5, 10, 9, 7, 3, 6, 1, 2, 4, 8, 5, 10, 9, 7, 3, 6, 1, 2, 4, 8, 5, 10, 9, 7

Offset

0,2

Comments

a(k) = k has only one solution, namely k=7. - Jon Perry, Oct 30 2014

As 2 is a primitive root of 11, all integers 1 through 10 are present. - Jon Perry, Oct 30 2014

References

H. Cohn, A Second Course in Number Theory, Wiley, NY, 1962, p. 256.

I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Wikipedia, Primitive roots

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,-1,1).

Formula

a(n) = a(n-1) - a(n-5) + a(n-6). - R. J. Mathar, Apr 13 2010

G.f.: (1+x+2*x^2+4*x^3-3*x^4+6*x^5)/ ((1-x) * (1+x) * (x^4-x^3+x^2-x+1)). - R. J. Mathar, Apr 13 2010

a(n+10) = a(n). - Jon Perry, Oct 30 2014

a(n+5) = 11 - a(n) for all n in Z. - Michael Somos, Oct 17 2018

Example

2^6 = 64 = 66 - 2 == -2 mod 11 == 9 mod 11, so a(6) = 9.

Maple

i := 5: [ seq(numtheory[primroot](ithprime(i))^j mod ithprime(i), j=0..100) ];

Mathematica

Table[Mod[2^n, 11], {n, 0, 6!}] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2010 *)

Prog

(Sage) [power_mod(2, n, 11) for n in range(0, 78)] # Zerinvary Lajos, Nov 03 2009
(PARI) a(n)=lift(Mod(2, 11)^n) \\ Charles R Greathouse IV, Jul 02 2013
(Magma) [Modexp(2, n, 11): n in [0..100]]; // G. C. Greubel, Oct 16 2018
(GAP) List([0..70], n->PowerMod(2, n, 11)); # Muniru A Asiru, Oct 18 2018

Crossrefs

Cf. A000079 (2^n), A008830, A168429.

Sequence in context: A227818 A300890 A021893 * A307357 A116624 A361191

Adjacent sequences: A036114 A036115 A036116 * A036118 A036119 A036120

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved