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A036117
a(n) = 2^n mod 11.
10
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.
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 A366304
KEYWORD
nonn,easy
STATUS
approved