A178591 -id:A178591 - cp's OEIS frontend

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

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, 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, 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

Offset: 0

Paul Barry, Apr 02 2004

From Klaus Brockhaus, May 30 2010: (Start)
Periodic sequence: Repeat [1, 1, 1, 3].
Continued fraction expansion of (9+sqrt(165))/14.
Decimal expansion of 371/3333. (End)
Final nonzero digit of n^n in base 4. - José María Grau Ribas, Jan 19 2012

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

Cf. A000045, A061347, A167816, A177704, A178591.

[1+2*0^((n+1) mod 4) : n in [0..100]]; // Wesley Ivan Hurt, Oct 23 2014

A093148:=n->1+2*0^(n+1 mod 4): seq(A093148(n), n=0..100); # Wesley Ivan Hurt, Oct 23 2014

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 *)
PadRight[{},120,{1,1,1,3}] (* Harvey P. Dale, Sep 03 2021 *)

a(n)=if(n%4==3,3,1) \\ Charles R Greathouse IV, Oct 07 2015

G.f.: (1+x+x^2+3*x^3)/(1-x^4); a(n) = 3/2-sin(Pi*n/2)-cos(Pi*n)/2.
From Klaus Brockhaus, May 30 2010: (Start)
a(n) = a(n-4) for n > 3; a(0) = a(1) = a(2) = 1, a(3) = 3.
a(n) = (3-(-1)^n+(1-(-1)^n)*i*i^n)/2 where i = sqrt(-1). (End)
a(n) = 1 + 2*0^mod(n+1, 4). - Wesley Ivan Hurt, Oct 23 2014

A178592 Decimal expansion of sqrt(165).

Original entry on oeis.org

1, 2, 8, 4, 5, 2, 3, 2, 5, 7, 8, 6, 6, 5, 1, 2, 9, 0, 2, 0, 1, 1, 6, 8, 9, 8, 4, 7, 7, 6, 3, 9, 9, 4, 0, 4, 1, 9, 4, 6, 7, 3, 5, 2, 5, 1, 1, 5, 6, 0, 2, 6, 3, 8, 7, 0, 2, 8, 6, 4, 7, 1, 2, 3, 4, 2, 5, 8, 5, 1, 9, 7, 0, 4, 7, 7, 7, 8, 2, 3, 4, 1, 1, 0, 2, 1, 8, 3, 6, 3, 4, 4, 3, 7, 8, 1, 1, 7, 2, 5, 6, 7, 3, 4, 5

Offset: 2

Klaus Brockhaus, May 30 2010

Continued fraction expansion of sqrt(165) is A010213.

			sqrt(165) = 12.84523257866512902011...

G. C. Greubel, Table of n, a(n) for n = 2..10001

Cf. A178591 (decimal expansion of (9+sqrt(165))/14), A010213 (12 followed by (repeat 1, 5, 2, 5, 1, 24)).

SetDefaultRealField(RealField(100)); Sqrt(165); // G. C. Greubel, Jan 30 2019

RealDigits[Sqrt[165],10,120][[1]] (* Harvey P. Dale, May 30 2012 *)

default(realprecision, 100); sqrt(165) \\ G. C. Greubel, Jan 30 2019

numerical_approx(sqrt(165), digits=100) # G. C. Greubel, Jan 30 2019

cp's OEIS Frontend

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

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