OFFSET
1,2
COMMENTS
Each element is coprime to preceding two elements. - Amarnath Murthy, Jun 12 2001
LINKS
Guenther Schrack, Table of n, a(n) for n = 1..10012
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
FORMULA
{k | k == 1, 2, 3, 5 (mod 6)}.
G.f.: x*(1 + x^2 + x^3) / ((1+x^2)*(1-x)^2). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, May 20 2016: (Start)
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4), for n>4.
a(n) = (6*n - 4 + i^(1-n) + i^(n-1))/4, where i = sqrt(-1).
E.g.f.: (2 + sin(x) + (3*x - 2)*exp(x))/2. - Ilya Gutkovskiy, May 21 2016
a(1-n) = - A047251(n). - Wesley Ivan Hurt, May 21 2016
From Guenther Schrack, Feb 16 2019: (Start)
a(n) = (6*n - 4 + (1 - (-1)^n)*(-1)^(n*(n-1)/2))/4.
a(n) = a(n-4) + 6, a(1)=1, a(2)=2, a(3)=3, a(4)=5, for n > 4.
a(n) = A047237(n) + 1. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 5*sqrt(3)*Pi/36 + log(2)/3 - log(3)/4. - Amiram Eldar, Dec 17 2021
a(n) = 2*n - 1 - floor(n/2) + floor(n/4) - floor((n+1)/4). - Ridouane Oudra, Feb 21 2023
EXAMPLE
After 21 and 23 the next term is 25 as 24 has a common divisor with 21.
MAPLE
MATHEMATICA
Select[Range[100], MemberQ[{1, 2, 3, 5}, Mod[#, 6]] &]
LinearRecurrence[{2, -2, 2, -1}, {1, 2, 3, 5}, 100] (* Harvey P. Dale, May 14 2020 *)
PROG
(Haskell)
a047255 n = a047255_list !! (n-1)
a047255_list = 1 : 2 : 3 : 5 : map (+ 6) a047255_list
-- Reinhard Zumkeller, Jan 17 2014
(Magma) [n : n in [0..100] | n mod 6 in [1, 2, 3, 5]]; // Wesley Ivan Hurt, May 21 2016
(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 2, -2, 2]^(n-1)*[1; 2; 3; 5])[1, 1] \\ Charles R Greathouse IV, Feb 11 2017
(Sage) a=(x*(1+x^2+x^3)/((1+x^2)*(1-x)^2)).series(x, 80).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Feb 16 2019
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Jun 15 2001
STATUS
approved