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A036124 a(n) = 2^n mod 37. 4
1, 2, 4, 8, 16, 32, 27, 17, 34, 31, 25, 13, 26, 15, 30, 23, 9, 18, 36, 35, 33, 29, 21, 5, 10, 20, 3, 6, 12, 24, 11, 22, 7, 14, 28, 19, 1, 2, 4, 8, 16, 32, 27, 17, 34, 31, 25, 13, 26, 15, 30, 23, 9, 18, 36, 35, 33, 29, 21, 5 (list; graph; refs; listen; history; text; internal format)
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

Cf. A000079 (2^n).

Sequence in context: A070348 A130670 A070340 * A070339 A070338 A331380

Adjacent sequences:  A036121 A036122 A036123 * A036125 A036126 A036127

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 21 21:14 EDT 2021. Contains 348155 sequences. (Running on oeis4.)