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A036118 a(n) = 2^n mod 13. 7
1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The sequence is 12-periodic.

REFERENCES

I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

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

FORMULA

a(n) = (1/132)*(79*(n mod 12) + 46*((n+1) mod 12) - 42*((n+2) mod 12) + 57*((n+3) mod 12) + 35*((n+4) mod 12) + 24*((n+5) mod 12) - 53*((n+6) mod 12) - 20*((n+7) mod 12) + 68*((n+8) mod 12) - 31*((n+9) mod 12) - 9*((n+10) mod 12) + 2*((n+11) mod 12)). - Paolo P. Lava, Nov 24 2006

a(n) = 13/2 + (-5/3 - (2/3)*sqrt(3))*cos(Pi*n/6) + (-1/3 - sqrt(3))*sin(Pi*n/6) - (13/6)*cos(Pi*n/2) - (13/6)*sin(Pi*n/2) + (-5/3 + (2/3)*sqrt(3))*cos(5*Pi*n/6) + (sqrt(3) - 1/3)*sin(5*Pi*n/6). - Richard Choulet, Dec 12 2008

a(n) = a(n-1) - a(n-6) + a(n-7). - R. J. Mathar, Apr 13 2010

G.f.: (1 + x + 2*x^2 + 4*x^3 - 5*x^4 + 3*x^5 + 7*x^6)/ ((1-x) * (x^2+1) * (x^4 - x^2 + 1)). - R. J. Mathar, Apr 13 2010

a(n) = 13 - a(n+6) = a(n+12) for all n in Z. - Michael Somos, Oct 17 2018

MAPLE

[ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];

MATHEMATICA

PowerMod[2, Range[0, 70], 13] (* Wesley Ivan Hurt, Nov 20 2014 *)

PROG

(Sage) [power_mod(2, n, 13) for n in range(0, 72)] # Zerinvary Lajos, Nov 03 2009

(PARI) a(n)=2^n%13 \\ Charles R Greathouse IV, Oct 07 2015

(MAGMA) [2^n mod 13: n in [0..100]]; // G. C. Greubel, Oct 16 2018

(GAP) List([0..95], n->PowerMod(2, n, 13)); # Muniru A Asiru, Jan 31 2019

CROSSREFS

Cf. A008831.

Sequence in context: A232645 A257470 A139080 * A247555 A340730 A101942

Adjacent sequences:  A036115 A036116 A036117 * A036119 A036120 A036121

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 22 11:49 EDT 2021. Contains 348168 sequences. (Running on oeis4.)