A158478 Number of colors needed to paint n sectors of a circle.

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, 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, 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

Offset

0,3

Comments

No pair of adjacent sectors can have the same color.

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

Links

Stefano Spezia, Table of n, a(n) for n = 0..10000

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

Formula

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

E.g.f.: 2*cosh(x) + 3*sinh(x) - 2*(1 + x). - Stefano Spezia, Mar 24 2020

Mathematica

Join[Range[0, 1], ConstantArray[{2, 3}, 20]] // Flatten (* Robert Price, Jun 15 2020 *)

Prog

(PARI) a(n)=if(n<4, n, 2+n%2)
(Haskell)
a158478 n = if n < 4 then n else 2 + mod n 2
a158478_list = [0..3] ++ cycle [2, 3]
-- Reinhard Zumkeller, Nov 30 2014

Crossrefs

Cf. A010693, A158411.

Cf. A020639, A098548.

Sequence in context: A368405 A356464 A010693 * A139713 A171465 A178620

Adjacent sequences: A158475 A158476 A158477 * A158479 A158480 A158481

Keyword

nonn

Author

Jaume Oliver Lafont, Mar 20 2009

Status

approved