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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved