OFFSET
1,2
COMMENTS
Original name was: Numbers that are congruent to {1, 2, 3, 4} mod 5.
More generally the sequence of numbers not divisible by some fixed integer m>=2 is given by a(n,m) = n-1+floor((n+m-2)/(m-1)). - Benoit Cloitre, Jul 11 2009
Complement of A008587. - Reinhard Zumkeller, Nov 30 2009
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
G.f.: (x+2*x^2+3*x^3+4*x^4+4*x^5+3*x^6+2*x^7+x^8)/(1-x^4)^2 (not reduced). - Len Smiley
a(n) = 5+a(n-4).
G.f.: x*(1+x+x^2+x^3+x^4)/((1-x)*(1-x^4)).
a(n) = n-1+floor((n+3)/4). - Benoit Cloitre, Jul 11 2009
a(n) = floor((15*n-1)/12). - Gary Detlefs, Mar 07 2010
a(n) = A225496(n) for n <= 42. - Reinhard Zumkeller, May 09 2013
From Wesley Ivan Hurt, Jun 22 2015: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5), n>5.
a(n) = (10*n-5-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))/8. (End)
E.g.f.: 1 + (1/4)*(-cos(x) + (-3 + 5*x)*cosh(x) + sin(x) + (-2 + 5*x)*sinh(x)). - Stefano Spezia, Dec 01 2019
a(n) = floor((5*n-1)/4). - Wolfdieter Lang, Sep 30 2020
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2-2/sqrt(5))*Pi/5 = A179290 * A019692 / 10. - Amiram Eldar, Dec 07 2021
MAPLE
seq(floor((15*n-1)/12), n=1..56); # Gary Detlefs, Mar 07 2010
MATHEMATICA
Select[Table[n, {n, 200}], Mod[#, 5]!=0&] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011 *)
PROG
(PARI) a(n)= n+(n-1)\4 \\ corrected by Michel Marcus, Sep 02 2022
(PARI) a(n)=n-1+floor((n+3)/4) \\ Benoit Cloitre, Jul 11 2009
(Sage) [i for i in range(72) if gcd(5, i) == 1] # Zerinvary Lajos, Apr 21 2009
(Haskell)
a047201 n = a047201_list !! (n-1)
a047201_list = [x | x <- [1..], mod x 5 > 0]
-- Reinhard Zumkeller, Dec 17 2011
(Magma) [Floor((15*n-1)/12): n in [1..70]]; // Vincenzo Librandi, Apr 06 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Comment from Lekraj Beedassy, Dec 17 2006 is now the current name. - Wesley Ivan Hurt, Jun 25 2015
STATUS
approved