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A093148 a(n) = gcd(Fibonacci(n+5), Fibonacci(n+1)).

%I A093148 #31 Sep 08 2022 08:45:13
%S A093148 1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,
%T A093148 1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,
%U A093148 1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1,1,1,3,1
%N A093148 a(n) = gcd(Fibonacci(n+5), Fibonacci(n+1)).
%C A093148 From _Klaus Brockhaus_, May 30 2010: (Start)
%C A093148 Periodic sequence: Repeat [1, 1, 1, 3].
%C A093148 Continued fraction expansion of (9+sqrt(165))/14.
%C A093148 Decimal expansion of 371/3333. (End)
%C A093148 Final nonzero digit of n^n in base 4. - _José María Grau Ribas_, Jan 19 2012
%H A093148 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F A093148 G.f.: (1+x+x^2+3*x^3)/(1-x^4); a(n) = 3/2-sin(Pi*n/2)-cos(Pi*n)/2.
%F A093148 From _Klaus Brockhaus_, May 30 2010: (Start)
%F A093148 a(n) = a(n-4) for n > 3; a(0) = a(1) = a(2) = 1, a(3) = 3.
%F A093148 a(n) = (3-(-1)^n+(1-(-1)^n)*i*i^n)/2 where i = sqrt(-1). (End)
%F A093148 a(n) = 1 + 2*0^mod(n+1, 4). - _Wesley Ivan Hurt_, Oct 23 2014
%p A093148 A093148:=n->1+2*0^(n+1 mod 4): seq(A093148(n), n=0..100); # _Wesley Ivan Hurt_, Oct 23 2014
%t A093148 f[n_] := Switch[Mod[n, 4], 0, 1, 1, 1, 2, 1, 3, 3]; Array[f, 105, 0] (* _Robert G. Wilson v_, Jan 23 2012 *)
%t A093148 PadRight[{},120,{1,1,1,3}] (* _Harvey P. Dale_, Sep 03 2021 *)
%o A093148 (Magma) [1+2*0^((n+1) mod 4) : n in [0..100]]; // _Wesley Ivan Hurt_, Oct 23 2014
%o A093148 (PARI) a(n)=if(n%4==3,3,1) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A093148 Cf. A000045, A061347, A167816, A177704, A178591.
%K A093148 easy,nonn
%O A093148 0,4
%A A093148 _Paul Barry_, Apr 02 2004