A036120 a(n) = 2^n mod 19.

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, 11, 3, 6, 12, 5, 10, 1, 2, 4, 8

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

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

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

Formula

From R. J. Mathar, Apr 13 2010: (Start)

a(n)= a(n-1) - a(n-9) + a(n-10).

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)). (End)

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

(SageMath) [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

Adjacent sequences: A036117 A036118 A036119 * A036121 A036122 A036123

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved