A062116 a(n) = 2^n mod 17.

1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13, 9, 1, 2, 4, 8, 16, 15, 13

Offset: 0

Author

Olivier Gérard, Jun 06 2001

Keywords

• nonn
• easy

Comments

Period 8.

Examples

			a(5) = 32 mod 17 = 15.
		

References

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

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,-1,1).

Crossrefs

Cf. A036117, A036118.

Programs

GAP

a:=List([0..70],n->PowerMod(2,n,17));; Print(a); # Muniru A Asiru, Jan 29 2019

Magma

[2^n mod 17: n in [0..100]]; // G. C. Greubel, Oct 16 2018

Mathematica

Mod[#,17]&/@(2^Range[0,100])  (* Harvey P. Dale, Mar 06 2011 *)

PARI

a(n) = { lift(Mod(2,17)^n) } \\ Harry J. Smith, Aug 01 2009

Sage

[power_mod(2,n,17) for n in range(0,87)] # Zerinvary Lajos, Nov 03 2009

Formula

From R. J. Mathar, Apr 13 2010: (Start)

a(n) = a(n-1) - a(n-4) + a(n-5).

G.f.: (1 + x + 2*x^2 + 4*x^3 + 9*x^4)/((1-x)*(1+x^4)). (End)

a(n) = 17 - a(n+4) = a(n+8) for all n in Z. - Michael Somos, Oct 17 2018