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

%I

%S 1,2,5,7,8,11,13,14,17,19,20,23,25,26,29,31,32,35,37,38,41,43,44,47,

%T 49,50,53,55,56,59,61,62,65,67,68,71,73,74,77,79,80,83,85,86,89,91,92,

%U 95,97,98,101,103,104,107,109,110,113,115,116,119,121,122,125

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

%C Numbers n such that Fibonacci(n) mod 4 = 1. - _Gary Detlefs_, Jun 01 2012

%H Vincenzo Librandi, <a href="/A047268/b047268.txt">Table of n, a(n) for n = 1..5000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).

%F From _Colin Barker_, Mar 13 2012

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

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

%F a(n) = 2*n-1-floor((n mod 3)/2). - _Gary Detlefs_, Jun 01 2012

%F From _Wesley Ivan Hurt_, Jun 10 2016: (Start)

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

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

%p 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

%t Select[Range[0,120], MemberQ[{1,2,5}, Mod[#,6]]&] (* _Vincenzo Librandi_, Apr 26 2012 *)

%o (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

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_

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Last modified November 12 19:41 EST 2019. Contains 329078 sequences. (Running on oeis4.)