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A036120
a(n) = 2^n mod 19.
6
1, 2, 4, 8, 16, 13, 7, 14, 9, 18, 17, 15, 11, 3, 6, 12, 5, 10, 1, 2, 4, 8, 16, 13, 7, 14, 9, 18, 17, 15, 11, 3, 6, 12, 5, 10, 1, 2, 4, 8, 16, 13, 7, 14, 9, 18, 17, 15, 11, 3, 6, 12, 5, 10, 1, 2, 4, 8, 16, 13, 7, 14, 9, 18, 17, 15
OFFSET
0,2
COMMENTS
The sequence can be generated via a(n) = A061762(a(n-1)). Apparently any other choice of the first element leads also to periodic sequences, with fixed points of A061762 as special cases. - Zak Seidov, Aug 22 2007
REFERENCES
I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, -1, 1).
FORMULA
a(n)= +a(n-1) -a(n-9) +a(n-10). - R. J. Mathar, Apr 13 2010
G.f.: (1+x+2*x^2+4*x^3+8*x^4-3*x^5-6*x^6+7*x^7-5*x^8+10*x^9)/ ((1-x) * (1+x) * (x^2- x+1) * (x^6-x^3+1)). - R. J. Mathar, Apr 13 2010
a(n) = a(n+18). - Vincenzo Librandi, Sep 09 2011
MAPLE
with(numtheory) ; i := pi(19) ; [ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];
MATHEMATICA
PowerMod[2, Range[0, 100], 19] (* G. C. Greubel, Oct 17 2018 *)
PROG
(Sage) [power_mod(2, n, 19) for n in range(0, 66)] # Zerinvary Lajos, Nov 03 2009
(PARI) a(n)=lift(Mod(2, 19)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(2, n, 19): n in [0..100]]; // G. C. Greubel, Oct 17 2018
(Python) for n in range(0, 100): print(int(pow(2, n, 19)), end=' ') # Stefano Spezia, Oct 17 2018
(GAP) List([0..60], n->PowerMod(2, n, 19)); # Muniru A Asiru, Oct 17 2018
CROSSREFS
CF. A000079 (2^n).
Sequence in context: A342072 A095915 A208278 * A334629 A358708 A108565
KEYWORD
nonn,easy
STATUS
approved