A047268 Numbers that are congruent to {1, 2, 5} mod 6.

1, 2, 5, 7, 8, 11, 13, 14, 17, 19, 20, 23, 25, 26, 29, 31, 32, 35, 37, 38, 41, 43, 44, 47, 49, 50, 53, 55, 56, 59, 61, 62, 65, 67, 68, 71, 73, 74, 77, 79, 80, 83, 85, 86, 89, 91, 92, 95, 97, 98, 101, 103, 104, 107, 109, 110, 113, 115, 116, 119, 121, 122, 125

Offset

1,2

Comments

Numbers n such that Fibonacci(n) mod 4 = 1. - Gary Detlefs, Jun 01 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

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

Formula

From Colin Barker, Mar 13 2012

G.f.: x*(1+x+3*x^2+x^3)/((1-x)^2*(1+x+x^2)).

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

a(n) = 2*n-1-floor((n mod 3)/2). - Gary Detlefs, Jun 01 2012

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

a(n) = (6*n-4+cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3.

a(3k) = 6k-1, a(3k-1) = 6k-4, a(3k-2) = 6k-5. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = (6-sqrt(3))*Pi/18 - log(2)/6. - Amiram Eldar, Dec 16 2021

Maple

A047268:=n->(6*n-4+cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3: seq(A047268(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 120], MemberQ[{1, 2, 5}, Mod[#, 6]]&] (* Vincenzo Librandi, Apr 26 2012 *)

Prog

(Magma) I:=[1, 2, 5, 7]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, Apr 26 2012

Crossrefs

Sequence in context: A153086 A032784 A277266 * A039580 A361461 A189296

Adjacent sequences: A047265 A047266 A047267 * A047269 A047270 A047271

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved