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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

CF. A000079 (2^n).

Programs

GAP

List([0..60],n->PowerMod(2,n,19)); # Muniru A Asiru, Oct 17 2018

Magma

[Modexp(2, n, 19): n in [0..100]]; // G. C. Greubel, Oct 17 2018

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 *)

PARI

a(n)=lift(Mod(2,19)^n) \\ Charles R Greathouse IV, Mar 22 2016

Python

for n in range(0, 100): print(int(pow(2, n, 19)), end=' ') # Stefano Spezia, Oct 17 2018

Sage

[power_mod(2,n,19) for n in range(0,66)] # Zerinvary Lajos, Nov 03 2009

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