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Period 2: repeat (3,5).
9

%I #45 Aug 04 2024 22:05:24

%S 3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,

%T 3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,

%U 3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5,3,5

%N Period 2: repeat (3,5).

%C From _Klaus Brockhaus_, Dec 10 2009: (Start)

%C Interleaving of A010701 and A010716.

%C Also continued fraction expansion of (15+sqrt(285))/10.

%C Also decimal expansion of 35/99.

%C Binomial transform of 3 followed by A084633 without initial terms 1,0.

%C Inverse binomial transform of A171497. (End)

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).

%F From _Klaus Brockhaus_, Dec 10 2009: (Start)

%F a(n) = a(n-2) for n > 1; a(0) = 3, a(1) = 5.

%F G.f.: (3+5*x)/((1-x)*(1+x)). (End)

%F a(n) = 4 - (-1)^n. - _Aaron J Grech_, Aug 02 2024

%F E.g.f.: 3*cosh(x) + 5*sinh(x). - _Stefano Spezia_, Aug 04 2024

%t Table[If[OddQ[n], 3, 5], {n, 1, 50}] (* _Stefan Steinerberger_, Apr 10 2006 *)

%t PadRight[{},120,{3,5}] (* _Harvey P. Dale_, Sep 03 2012 *)

%o (Magma) &cat[ [3, 5]: n in [1..53] ]; // _Klaus Brockhaus_, Dec 10 2009

%o (PARI) a(n)=3+n%2*2 \\ _Charles R Greathouse IV_, Nov 20 2011

%Y Cf. A010701 (all 3's sequence), A010716 (all 5's sequence), A084633 (inverse binomial transform of repeated odd numbers), A171497.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_