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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000079 (2^n).

Programs

GAP

List([0..65],n->PowerMod(2,n,37)); # Muniru A Asiru, Oct 18 2018

Magma

[Modexp(2, n, 37): n in [0..100]]; // G. C. Greubel, Oct 16 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 *)

PARI

a(n)=lift(Mod(2,37)^n) \\ Charles R Greathouse IV, Mar 22 2016

Sage

[power_mod(2,n,37) for n in range(0,60)] # - Zerinvary Lajos, Nov 03 2009

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