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n^3 mod 8; the periodic sequence {0,1,0,3,0,5,0,7}.
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%I #22 Dec 14 2023 05:18:51

%S 0,1,0,3,0,5,0,7,0,1,0,3,0,5,0,7,0,1,0,3,0,5,0,7,0,1,0,3,0,5,0,7,0,1,

%T 0,3,0,5,0,7,0,1,0,3,0,5,0,7,0,1,0,3,0,5,0,7,0,1,0,3,0,5,0,7,0,1,0,3,

%U 0,5,0,7,0,1,0,3,0,5,0,7,0,1,0,3,0,5,0,7,0,1,0,3,0,5,0,7,0,1,0,3,0,5,0,7,0

%N n^3 mod 8; the periodic sequence {0,1,0,3,0,5,0,7}.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 1).

%F G.f. = (x+3x^3+5x^5+7x^7)/(1-x^8)

%o (Sage) [power_mod(n,3,8 ) for n in range(0, 105)] # - _Zerinvary Lajos_, Oct 29 2009

%o (PARI) a(n)=n^3%8 \\ _Charles R Greathouse IV_, Apr 06 2016

%Y Cf. n mod 8 = A010877; n^2 mod 8 = A070432.

%K easy,nonn

%O 0,4

%A Bruce Corrigan (scentman(AT)myfamily.com), Aug 11 2005