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A070431 a(n) = n^2 mod 6. 20
0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(m*n) = a(m)*a(n) mod 6; a(3*n+k) = a(3*n-k) for k <= 3*n. - Reinhard Zumkeller, Apr 24 2009

Equivalently n^6 mod 6. - Zerinvary Lajos, Nov 06 2009

Equivalently: n^(2*m + 2) mod 6; n^4 mod 6 is A070511; See formulas in A070511. - G. C. Greubel, Apr 01 2016

LINKS

Table of n, a(n) for n=0..100.

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

FORMULA

G.f.: -x*(1+4*x+3*x^2+4*x^3+x^4)/((x-1)*(1+x)*(1+x+x^2)*(x^2-x+1)). - R. J. Mathar, Jul 23 2009

a(n) = a(n-6). - Reinhard Zumkeller, Apr 24 2009

MAPLE

A070431:=n->n^2 mod 6: seq(A070431(n), n=0..100); # Wesley Ivan Hurt, Apr 01 2016

MATHEMATICA

Table[Mod[n^2, 6], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)

LinearRecurrence[{0, 0, 0, 0, 0, 1}, {0, 1, 4, 3, 4, 1}, 101] (* Ray Chandler, Aug 26 2015 *)

PROG

(Sage) [power_mod(n, 2, 6) for n in xrange(0, 101)] # Zerinvary Lajos, Oct 30 2009

(Sage) [power_mod(n, 6, 6) for n in xrange(0, 101)] # Zerinvary Lajos, Nov 06 2009

(PARI) a(n)=n^2%6 \\ Charles R Greathouse IV, Sep 24 2015

(MAGMA) [n^2 mod 6 : n in [0..100]]; // Wesley Ivan Hurt, Apr 01 2016

(MAGMA) [Modexp(n, 2, 6): n in [0..100]]; // Vincenzo Librandi, Apr 02 2016

CROSSREFS

Cf. A000290, A008959, A070435, A070438, A070442, A070452, A070511, A159852.

Sequence in context: A243149 A048156 * A070511 A066340 A195597 A143505

Adjacent sequences:  A070428 A070429 A070430 * A070432 A070433 A070434

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 12 2002

STATUS

approved

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Last modified November 24 00:27 EST 2017. Contains 295164 sequences.