

A109718


Periodic sequence with period {0,1,0,3}, or n^3 mod 4.


3



0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0
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OFFSET

0,4


COMMENTS

Since n^(2k+1) mod 4 = n^3 mod 4 for k>1 this sequence also represents n^5 mod 4; and n^7 mod 4; etc.


LINKS

Table of n, a(n) for n=0..104.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).


FORMULA

a(n) = n^3 mod 4.
G.f. = (x+3*x^3)/(1x^4).
a(n) = (1/12)*(11*(n mod 4)  7*((n+1) mod 4) + 5*((n+2) mod 4)  ((n+3) mod 4)).  Paolo P. Lava, Nov 21 2006
a(n) = (n mod 2)*(n mod 4) = (1+(1)^(n+1))*(2+i^(n+1))/2 with i=sqrt(1).  Bruno Berselli, Mar 14 2011


PROG

(Sage) [power_mod(n, 3, 4 )for n in range(0, 105)] # Zerinvary Lajos, Oct 29 2009
(Magma) &cat[[0, 1, 0, 3]: k in [0..26]]; // Bruno Berselli, Mar 14 2011
(PARI) a(n)=n^3%4 \\ Charles R Greathouse IV, Apr 06 2016


CROSSREFS

n mod 4 = A010873; n^2 mod 4 = A000035.
Cf. A110270; A131743.  Bruno Berselli, Mar 14 2011
Sequence in context: A357868 A357881 A204689 * A053385 A213543 A247254
Adjacent sequences: A109715 A109716 A109717 * A109719 A109720 A109721


KEYWORD

easy,nonn


AUTHOR

Bruce Corrigan (scentman(AT)myfamily.com), Aug 09 2005


STATUS

approved



