OFFSET
0,2
REFERENCES
I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Asaad Nabil AlSharif, Plot of points on a circle
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).
FORMULA
a(n) = +a(n-1) -a(n-18) +a(n-19). - R. J. Mathar, Feb 06 2011
G.f.: ( -1 -x -2*x^2 -4*x^3 -8*x^4 -16*x^5 +5*x^6 +10*x^7 -17*x^8 +3*x^9 +6*x^10 +12*x^11 -13*x^12 +11*x^13 -15*x^14 +7*x^15 +14*x^16 -9*x^17 -19*x^18 ) / ( (x-1) *(x^2+1) *(x^4-x^2+1)*(x^12-x^6+1) ). - R. J. Mathar, Feb 06 2011
a(n) = a(n+36). - R. J. Mathar, Jun 04 2016
a(n) = 37 - a(n+18) for all n in Z. - Michael Somos, Oct 17 2018
MAPLE
i := pi(37) ; [ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];
MATHEMATICA
PowerMod[2, Range[0, 60], 37] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1}, {1, 2, 4, 8, 16, 32, 27, 17, 34, 31, 25, 13, 26, 15, 30, 23, 9, 18, 36}, 60] (* Harvey P. Dale, Jul 03 2017 *)
PROG
(Sage) [power_mod(2, n, 37) for n in range(0, 60)] # - Zerinvary Lajos, Nov 03 2009
(PARI) a(n)=lift(Mod(2, 37)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(2, n, 37): n in [0..100]]; // G. C. Greubel, Oct 16 2018
(GAP) List([0..65], n->PowerMod(2, n, 37)); # Muniru A Asiru, Oct 18 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved