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Number of colors needed to paint n sectors of a circle.
10

%I #32 Sep 03 2024 15:10:40

%S 0,1,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,

%T 2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,

%U 2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2

%N Number of colors needed to paint n sectors of a circle.

%C No pair of adjacent sectors can have the same color.

%C For n > 0: smallest prime factor of A098548(n).

%C Decimal expansion of 61/4950. - _Elmo R. Oliveira_, May 05 2024

%H Stefano Spezia, <a href="/A158478/b158478.txt">Table of n, a(n) for n = 0..10000</a>

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

%F G.f.: x*(1+2*x+2*x^2)/(1-x^2).

%F E.g.f.: 2*cosh(x) + 3*sinh(x) - 2*(1 + x). - _Stefano Spezia_, Mar 24 2020

%F a(n) = a(n-2) for n > 3. - _Elmo R. Oliveira_, May 05 2024

%F a(n) = (n mod 2) + (2 mod (n+1)). - _Aaron J Grech_, Sep 02 2024

%t Join[Range[0, 1], ConstantArray[{2, 3}, 20]] // Flatten (* _Robert Price_, Jun 15 2020 *)

%o (PARI) a(n)=if(n<4,n,2+n%2)

%o (Haskell)

%o a158478 n = if n < 4 then n else 2 + mod n 2

%o a158478_list = [0..3] ++ cycle [2,3]

%o -- _Reinhard Zumkeller_, Nov 30 2014

%Y Cf. A010693, A020639, A098548, A158411.

%K nonn

%O 0,3

%A _Jaume Oliver Lafont_, Mar 20 2009