A047254 - OEIS

A047254

Numbers that are congruent to {2, 3, 5} mod 6.

2, 3, 5, 8, 9, 11, 14, 15, 17, 20, 21, 23, 26, 27, 29, 32, 33, 35, 38, 39, 41, 44, 45, 47, 50, 51, 53, 56, 57, 59, 62, 63, 65, 68, 69, 71, 74, 75, 77, 80, 81, 83, 86, 87, 89, 92, 93, 95, 98, 99, 101, 104, 105, 107, 110, 111, 113, 116, 117, 119, 122, 123, 125, 128, 129

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OFFSET

1,1

COMMENTS

For n>0: a(n) = greatest m<=2*(n+1) coprime to a(n-1). - Reinhard Zumkeller, Oct 31 2005

LINKS

Table of n, a(n) for n=1..65.

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

FORMULA

G.f.: x*(x+2)*(1+x^2) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jun 10 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = (6*n-2-cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3.

a(3k) = 6k-1, a(3k-1) = 6k-3, a(3k-2) = 6k-4. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = (3+2*sqrt(3))*Pi/36 - log(2+sqrt(3))/(2*sqrt(3)) + log(2)/6. - Amiram Eldar, Dec 16 2021

MAPLE

A047254:=n->(6*n-2-cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3: seq(A047254(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

MATHEMATICA

Select[Range[0, 150], MemberQ[{2, 3, 5}, Mod[#, 6]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)

PROG

(Magma) [n: n in [0..150] | n mod 6 in {2, 3, 5} ]; // Vincenzo Librandi, Dec 25 2010

CROSSREFS

Sequence in context: A027756 A119863 A285253 * A226815 A284890 A051214

Adjacent sequences: A047251 A047252 A047253 * A047255 A047256 A047257

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved