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A047268 Numbers that are congruent to {1, 2, 5} mod 6. 1
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 (list; graph; refs; listen; history; text; internal format)
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)

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 A189296 A051279

Adjacent sequences:  A047265 A047266 A047267 * A047269 A047270 A047271

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 21 11:05 EDT 2019. Contains 328294 sequences. (Running on oeis4.)