

A257164


Period 5 sequence: repeat [0, 2, 4, 1, 3].


1



0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 2
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OFFSET

0,2


COMMENTS

Label the vertices of a regular pentagon from 0..4 going clockwise. Then, starting at vertex "0", a(n) gives the order in which the vertices must be connected to draw a clockwise inscribed, 5pointed star that remains unbroken during construction.


LINKS

Table of n, a(n) for n=0..66.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).


FORMULA

a(n) = (2n mod 5) = A010874(A005843(n)).
G.f.: x*(2+4*x+x^2+3*x^3)/(1x^5).
Recurrence: a(n) = a(n5).
a(n) = a(a(a(a(a(n))))).
a(n) = A010874(3n) = a(a(a(n))).
Bisections: a(2n) = A010874(n) = a(a(n)); a(2n+1) = A010874(2n).
Trisections: a(3n) = A010874(n) = a(a(a(a(n)))); a(3n+1) = A010874(n+2); a(3n+2) = A010874(n1).


EXAMPLE

0 > 2 > 4 > 1 > 3 > ..repeat


MAPLE

A257164:=n>(2*n mod 5): seq(A257164(n), n=0..100);


MATHEMATICA

Mod[2 Range[0, 100], 5] (* or *)
CoefficientList[Series[x (2 + 4 x + x^2 + 3 x^3)/(1  x^5), {x, 0, 100}], x]
LinearRecurrence[{0, 0, 0, 0, 1}, {0, 2, 4, 1, 3}, 105] (* or *)
NestList[# /. {0 > 2, 1 > 3, 2 > 4, 3 > 0, 4 > 1} &, {0}, 104] // Flatten (* Robert G. Wilson v, Apr 30 2015 *)


PROG

(MAGMA) [(2*n mod 5) : n in [0..100]];
(PARI) a(n)=2*n%5 \\ Charles R Greathouse IV, Apr 21 2015


CROSSREFS

Cf. A005843.
Bisection of A010874.
Sequence in context: A050980 A053451 A254076 * A190555 A141843 A130266
Adjacent sequences: A257161 A257162 A257163 * A257165 A257166 A257167


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Apr 16 2015


STATUS

approved



