A070438 a(n) = n^2 mod 15.

0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6

Offset

0,3

Comments

Equivalently, n^6 mod 15. - Ray Chandler, Dec 27 2023

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

From Reinhard Zumkeller, Apr 24 2009: (Start)

a(m*n) = a(m)*a(n) mod 15.

a(15*n+7+k) = a(15*n+8-k) for k <= 15*n+7.

a(15*n+k) = a(15*n-k) for k <= 15*n.

a(n+15) = a(n). (End)

From R. J. Mathar, Mar 14 2011: (Start)

a(n) = a(n-15).

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

G.f.: (x^14 +4*x^13 +9*x^12 +x^11 +10*x^10 +6*x^9 +4*x^8 +4*x^7 +6*x^6 +10*x^5 +x^4 +9*x^3 +4*x^2 +x)/(-x^15 +1). - Colin Barker, Aug 14 2012

Mathematica

Table[Mod[n^2, 15], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1}, 97] (* Ray Chandler, Aug 26 2015 *)

Prog

(Sage) [power_mod(n, 2, 15)for n in range(0, 97)] # Zerinvary Lajos, Nov 06 2009
(PARI) a(n)=n^2%15 \\ Charles R Greathouse IV, Sep 28 2015

Crossrefs

Cf. A000290, A008959, A010378, A070431, A070435, A070442, A070452, A159852.

Row 15 of A048152.

Sequence in context: A199788 A197266 A200393 * A070638 A236104 A152205

Adjacent sequences: A070435 A070436 A070437 * A070439 A070440 A070441

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved