A036124 a(n) = 2^n mod 37.

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

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