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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 (list; graph; refs; listen; history; text; internal format)
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

CF. A000079 (2^n).

Sequence in context: A342072 A095915 A208278 * A334629 A108565 A066005

Adjacent sequences:  A036117 A036118 A036119 * A036121 A036122 A036123

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 21 21:25 EDT 2021. Contains 348155 sequences. (Running on oeis4.)