A167166 a(n) = n^7 mod 16.

0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0

Offset: 0

Author

Zerinvary Lajos, Oct 29 2009

Keywords

• nonn
• easy

Comments

Equivalently: n^(4*m+7) mod 16. - G. C. Greubel, Jun 04 2016

Links

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

Programs

Mathematica

Table[Mod[n^7, 16], {n, 0, 10}] (* G. C. Greubel, Jun 04 2016 *)
PowerMod[Range[0,100],7,16] (* or *) PadRight[{},100,{0,1,0,11,0,13,0,7,0,9,0,3,0,5,0,15}] (* Harvey P. Dale, Jul 29 2018 *)

PARI

a(n)=n^7%16 \\ Charles R Greathouse IV, Apr 06 2016

Sage

[power_mod(n,7,16)for n in range(0, 93)] #

Formula

From R. J. Mathar, Sep 30 2013: (Start)

a(n) = a(n-16).

G.f. -x*(1 +11*x^2 +13*x^4 +7*x^6 +9*x^8 +3*x^10 +5*x^12 +15*x^14) / ( (x-1)*(1+x)*(1+x^2)*(1+x^4)*(1+x^8) ). (End)

a(n) = A130909(A001015(n)). - Michel Marcus, Jun 04 2016